32-尺规作图
一、单选题
单选题
|
适中(0.65)
对于题目:“已知
,用直尺和圆规作出
的平分线
”,有以下四种作法,其中作法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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单选题
|
较难(0.4)
您最近一年使用:0次
单选题
|
适中(0.65)
名校
如图,在中,以点A为圆心,以适当长为半径作弧,分别交
,
于点E,F,再分别以E、F为圆心,以相同长度为半径作弧,两弧相交于点O,P为射线
上任意一点,过点P作
,交
于点M,连接
,若
,
,则
长度的最小值为( )
A.![]() | B.![]() | C.4 | D.![]() |
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11卷引用:2022年山东省济南市历下区东方双语实验学校中考数学三模试题
2022年山东省济南市历下区东方双语实验学校中考数学三模试题2023年山东省济南市章丘区中考一模数学试题2023年 山东省济南市商河县中考二模数学试题(已下线)2023年广东省深圳中学共同体中考模拟数学试题(6月)2023年安徽省安庆市第二中学中考二模数学试题(已下线)专题08 几何最值问题(针对第10题)(真题2题模拟60题)-学易金卷:5年(2019-2023)中考1年模拟数学真题分项汇编(安徽专用)2023年山东省青岛市高新区中考一模数学模拟试题辽宁省东北育才学校2023-2024学年九年级下学期调研考试数学试题(已下线)专题18.18 勾股定理(最短路径问题)(巩固篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(沪科版)(已下线)专题17.18 勾股定理(最短路径问题)(巩固篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(人教版)32-尺规作图
单选题
|
较难(0.4)
名校
如图,在
的内切圆(圆心为点
)与各边分别相切于点
,
,
,连接
,
,
.以点
为圆心,以适当长为半径作弧分别交
,
于
,
两点;分别以点
,
为圆心,以大于
的长为半径作弧,两条弧交于点
;作射线
.下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/108212ef-8e09-4688-b332-21fc4a1de299.png?resizew=234)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f01b7488c22afe63b1b80e27169bfdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/108212ef-8e09-4688-b332-21fc4a1de299.png?resizew=234)
A.点![]() ![]() ![]() ![]() |
B.点![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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5卷引用:天津市和平区2023-2024学年九年级上学期期末数学试题
单选题
|
较难(0.4)
如图,在
中,
,
,
,以点
为圆心,2为半径作
,与
交于点
,点
是
上一点,连接
,根据尺规作图得到点
,连接
,
,当
,
重合时,点
也与点
重合,有下列两种说法:
I:
的最大值为2;
II:
的面积的最大值为7.
下列判断正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/16/bd5e909c-f9b5-4e59-bf4d-d4996a6b48f7.png?resizew=174)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3dfcd8aff269dd5aba398816490c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ba1df94176a1f769c7a0a12bf357fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
I:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
II:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
下列判断正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/16/bd5e909c-f9b5-4e59-bf4d-d4996a6b48f7.png?resizew=174)
A.I,II都正确 | B.I,II都不正确 | C.I正确,II不正确 | D.I不正确,II正确 |
您最近一年使用:0次
单选题
|
较难(0.4)
如图,在平行四边形
中,以A为圆心,
长为半径画弧交
于点
,分别以点
为圆心,大于
的长为半径画弧,两弧交于点
,连接
并延长交
于点
,连接
交
于点
,过点A作
于点
,连接
.若
,则下列结论:①四边形
是菱形;②
;③
;④
;⑤
正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/3837a23c-f69a-47dd-9aab-a50c50c8daee.png?resizew=202)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65601b45c42faaf78ed5b703af67891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40fe477aea662f3ae9b6d28f1e785147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4744b427f036dfbc6db68c87cd5c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cd68cc82e90a5e2049a7ea3171b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584aea12933df2cd6dc3c2d07b608c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d30cd3e53a9df24fe6da5e8a3a7ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3899f8468ad52b921df16f55a0dbc804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37f782e16835bba3fb9f66e5fc93bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7b685260f7915514b0d239ff50005.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/3837a23c-f69a-47dd-9aab-a50c50c8daee.png?resizew=202)
A.①③④ | B.①③⑤ | C.②③④⑤ | D.①②③④⑤ |
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单选题
|
较难(0.4)
如图,矩形ABCD中,AB=10,BC=6,分别以C,D为圆心,以大于
的长为半径作弧,两弧分别交于G,H两点,作直线GH交CD于点E,连接AE,点D关于AE的对称点为点M,作射线AM交BC于点N,则CN的长为( )
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966690506113024/2968762916126720/STEM/54282a9f-1ebe-4f7f-b2f8-dc588875ef7d.png?resizew=253)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b840be5852709e18ea985954545e78d.png)
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966690506113024/2968762916126720/STEM/54282a9f-1ebe-4f7f-b2f8-dc588875ef7d.png?resizew=253)
A.![]() | B.4 | C.![]() | D.5 |
您最近一年使用:0次
单选题
|
适中(0.65)
名校
如图,
中,
,一同学利用直尺和圆规完成如下操作:
![](https://img.xkw.com/dksih/QBM/2022/4/23/2970037707579392/2977216612491264/STEM/d0726603d63545dca5593c829aac1a38.png?resizew=312)
①以点C为圆心,以CB为半径画弧,交AB于点G;分别以点G、B为圆心,以大于
的长为半径画弧,两弧交点K,作射线CK;
②以点B为圆心,以适当的长为半径画弧,交BC于点M,交AB的延长线于N,分别以M、N为圆心,以大于
的长为半径画弧,两弧交于点P,作直线BP交AC的延长线于点D,交射线CK于点E.
请你观察图形,根据操作结果解答下列问题;过点D作
交AB的延长线于点F,若
,
,则CE的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://img.xkw.com/dksih/QBM/2022/4/23/2970037707579392/2977216612491264/STEM/d0726603d63545dca5593c829aac1a38.png?resizew=312)
①以点C为圆心,以CB为半径画弧,交AB于点G;分别以点G、B为圆心,以大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edf0f7861974094f96a5c9213678cd6.png)
②以点B为圆心,以适当的长为半径画弧,交BC于点M,交AB的延长线于N,分别以M、N为圆心,以大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94e1ca12da27075e5241b7c7ce74672.png)
请你观察图形,根据操作结果解答下列问题;过点D作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa30a9ee227af2b387cf6e028c20d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0763b031b7e6b6d87ce3554ac482d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
A.13 | B.![]() | C.![]() | D.![]() |
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2022年河南省郑州外国语中学九年级(一模)数学试题2023年河南省驻马店市学业水平考试九年级数学试题(已下线)专题1.11 勾股定理与方程思想(专项练习)-2022-2023学年八年级数学上册基础知识专项讲练(北师大版)(已下线)专题2.23 勾股定理与方程思想(专项练习)-2022-2023学年八年级数学上册基础知识专项讲练(浙教版)32-尺规作图
单选题
|
适中(0.65)
如图,在矩形ABCD中,AB=8,BC=6,以B为圆心,适当的长为半径画弧,交BD,BC于M,N两点;再分别以M,N为圆心,大于
MN的长为半径画弧,两弧交于点P,作射线BP交CD于点F;再以B为圆心,BD的长为半径画弧,交射线BP于点E,则EF的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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单选题
|
较难(0.4)
如图,在
中,
,
.按照如下步骤作图:
为圆心,大于
的长为半径作弧,两弧相交于点
;
②作直线
,交
点
;
③以
为圆心,
长为半径作弧,交
的延长线于点
;
④连接
.
下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee54b9b398ce80cd054b56173fe810f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93148adbc6e856da9a9d263f485d003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
②作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
③以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
④连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c94c0af99f1996d8447f2b004805dba.png)
下列说法错误的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
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8卷引用:2023年江苏省南通市通州区、如东县中考二模数学试题
2023年江苏省南通市通州区、如东县中考二模数学试题广东省广州市天河区2023-2024学年九年级下学期开学考试数学试题2024年江苏省无锡冲刺中考数学模拟预测题山东省德州市齐河县表白寺镇中学2023-2024学年九年级下学期第一次月考数学试题(已下线)专题08 几何作图问题1-2024年中考数学二轮热点题型归纳与变式演练(江苏专用)2024年山东省泰安市东平县中考二模数学试题23-相似三角形32-尺规作图
二、填空题
填空题
|
较难(0.4)
如图,直线
,直线
分别与
、
相交于点
、
.小亮同学利用尺规按以下步骤作图:①以点
为圆心,以任意长为半径作弧交
于点
,交
于点
;②分别以
、
为圆心,以大于
长为半径作弧,两弧在
内交于点
;③作射线
交
于点
.若
,
,则
的内切圆半径长等于__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43ea8d9c712a465e7dfde8c1c1b6449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b840be5852709e18ea985954545e78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052b9d734309d97fd60c1d491a860dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b38a71ea8963e93f727ed2d42785ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b929a31d169a811004f0ecd6b7984e61.png)
![](https://img.xkw.com/dksih/QBM/2020/3/6/2413863481425920/2414517311864832/STEM/607eca673dbf4083ad9b8f6bbc4dc116.png?resizew=216)
您最近一年使用:0次
2020-03-07更新
|
415次组卷
|
3卷引用:2019年山东省潍坊市临朐县九年级数学中考三模试题
填空题
|
困难(0.15)
如图,在
中,以点
为圆心,以任意长为半径画弧,分别与边
交于点
分别以点
为圆心,大于
的长为半径画弧,两弧交于点
,作射线
交边
于点
,若点
为射线
上一动点,连接
,直线
交边
于点
,取线段
的中点
,连接
,若
,
,
,则边
的长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c0ecf2aeda1219e40e8db1bd73e063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94e1ca12da27075e5241b7c7ce74672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3f47f7c8e18b5e501c9bddeda0a547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f1c40ebcc993a5778478154c124f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b03bb56c7e76954b192bd8595a0865a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2023/9/13/3323760056303616/3327511070244864/STEM/286daa080d5e407eb090960ae0006d23.png?resizew=191)
您最近一年使用:0次
填空题
|
较难(0.4)
真题
如图,在
中,
,
,
,按下列步骤作图:①在
和
上分别截取
、
,使
.②分别以点D和点E为圆心,以大于
的长为半径作弧,两弧在
内交于点M.③作射线
交
于点F.若点P是线段
上的一个动点,连接
,则
的最小值是______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb01d2b57580731c8b807ac8cffc8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d212c1709b8e72a055cf1b5381ef64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65026a6b6402cb599e14be8023a3f6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad36eefc2a8f0e3f420e61d6e856d11c.png)
您最近一年使用:0次
2023-08-04更新
|
1406次组卷
|
16卷引用:2023年辽宁省锦州市中考数学真题
2023年辽宁省锦州市中考数学真题辽宁省阜新市太平区第四中学2023-2024学年九年级上学期12月月考数学试题2024年湖北省孝感市高新区中考一模数学试题2024年湖北省黄石市阳新县陶港中学中考模拟数学试题(已下线)查补培优冲刺02 几何最值类综合压轴-【查漏补缺】2024年中考数学复习冲刺过关(江苏专用)2024年北京市北京师范大学附属实验中学分校中考二模数学试题2024年江苏省连云港市赣榆实验中学等校中考三模数学试题湖北省黄石市阳新县陶港中学2023-2024学年九年级下学期月考数学试题32-尺规作图(已下线)专题1.15 角平分线(直通中考)(综合练)-2023-2024学年八年级数学下册基础知识专项突破讲与练(北师大版)(已下线)第1讲 几何初步(已下线)专题17.14 勾股定理(全章直通中考)(综合练)-2023-2024学年八年级数学下册基础知识专项突破讲与练(人教版)(已下线)重难点06几何最值问题(5大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(全国通用)(已下线)培优冲刺04 几何最值问题综合(4题型)-【查漏补缺】2024年中考数学复习冲刺过关(全国通用)(已下线)暑假作业02 线段的垂直平分线与角平分线-【暑假分层作业】2024年八年级数学暑假培优练(北师大版)(已下线)暑假作业11 三角形和平行四边形中的最值问题和动点问题-【暑假分层作业】2024年八年级数学暑假培优练(北师大版)
填空题
|
较难(0.4)
名校
如图,在矩形ABCD中,AB=1,AD=3.①以点A为圆心,以不大于AB长为半径作弧,分别交边AD,AB于点E,F,再分别以点E,F为圆心,以大于
EF长为半径作弧,两弧交于点P,作射线AP分别交BD,BC于点O,Q;②分别以点C,Q为圆心,以大于
CQ长为半径作弧,两弧交于点M,N,作直线MN交AP于点G,则OG长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/050e432c-2844-430c-ac33-534ce2425dc2.png?resizew=236)
您最近一年使用:0次
2022-04-15更新
|
389次组卷
|
5卷引用:湖南省长沙市雨花区一中雨花新华都学校2021-2022学年九年级下学期期中数学试题
填空题
|
较难(0.4)
在
中,
,
,以点
为圆心,适当长度为半径作弧,分别交
,
于点
,
,再以
,
为圆心,以大于
的长为半径作弧,两弧交于点
,作射线
,交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/25/1da8bfbd-4b69-4b45-8256-e7c5c721916a.png?resizew=378)
(1)如图1,若
,则线段
的长为______ ;
(2)如图2,在(1)的条件下,若点
为射线
上(
外)一动点,且
,则
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392b9e1a179a6676362679354a9e7e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94e1ca12da27075e5241b7c7ce74672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/25/1da8bfbd-4b69-4b45-8256-e7c5c721916a.png?resizew=378)
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)如图2,在(1)的条件下,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a665ba024f2840ce5aef3765249341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
您最近一年使用:0次
填空题
|
困难(0.15)
名校
如图,在每个边长为
的小正方形网格中,点
,
均在格点上,以
为直径作圆,点
为
的中点.
的长度等于___ ;
(2)请用无刻度的直尺,在圆上找一点
,使得
,并简要说明点
的位置是如何找到的(不要求证明)
______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)请用无刻度的直尺,在圆上找一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a29464f13d93ea6270d2708a83104cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2022-04-30更新
|
1149次组卷
|
8卷引用:2022年天津市河北区九年级中考一模数学试卷
2022年天津市河北区九年级中考一模数学试卷天津市南开翔宇学校2022-2023学年九年级下学期3月月考数学试卷天津市河西区2022-2023学年九年级下学期结课考试数学试卷2023年天津市新华中学中考一模数学试题天津市河东区2023-2024学年九年级下学期结课考试数学试题(已下线)2023年天津一模(网格作图)32-尺规作图(已下线)热点09 尺规作图(7大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(全国通用)
三、解答题
解答题-证明题
|
困难(0.15)
如图,已知
中,
,
,
,
是
上的一点,
,点
是线段
上的一个动点,沿
折叠
,点
与
重合,连接
.
![](https://img.xkw.com/dksih/QBM/2022/4/27/2967223074496512/2970900343537664/STEM/2461e767-ff92-42ab-b56d-7a1e33f67142.png?resizew=710)
(1)求证:
;
(2)若点
是
上的一点,且
,
①若
与
的面积比是
,请用无刻度的直尺和圆规在图(2)中作出折叠后的
(保留作图痕迹,不写作法);
②求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d2eae98e1683fbb9533584450dd696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d649afbddd907f0dfec1420f02f82fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d2231c7a2875ab6d423dff3ead4069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba47906b1c55990f2c0ca31d656b774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://img.xkw.com/dksih/QBM/2022/4/27/2967223074496512/2970900343537664/STEM/2461e767-ff92-42ab-b56d-7a1e33f67142.png?resizew=710)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c439d363860f3c9a636eec6b755754.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7cc5c75476896a599093f5ac10b97d.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34cd013d5aa08023f030e678ae9df355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8f9ef1bacc062fdb1e1b578b1db911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f38fdbe1b564976c606e57abfa93d0.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd0a51dbd657033a5f34ac1eaf0b6b7.png)
您最近一年使用:0次
2022-05-02更新
|
395次组卷
|
3卷引用:2022年江苏省泰兴市九年级数学一模试题
操作探究题
(1)已知
是半圆
的直径,
(
是正整数,且
不是3的倍数)是半圆
的一个圆心角.
操作:如图1,分别将半圆
的圆心角
(
取1、4、5、10)所对的弧三等分(要求:仅用圆规作图,不写作法,保留作图痕迹);
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/1392d841-3d2d-4c18-942d-f72f596c0f89.png?resizew=402)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/a3ab480c-a13e-4637-8c1d-3bb49307a35e.png?resizew=458)
交流:当
时,可以仅用圆规将半圆
的圆心角
所对的弧三等分吗?
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/ab5272e3-17a6-48ba-b057-530a280b9903.png?resizew=517)
探究:你认为当
满足什么条件时,就可以仅用圆规将半圆
的圆心角
所对的弧三等分?说说你的理由.
(2)如图2,
的圆周角
.为了将这个圆的圆周 14等分,请作出它的一条14等分弧
(要求:仅用圆规作图,不写作法,保留作图痕迹).
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beae93062eb8d79570ec05eec3fda9ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
操作:如图1,分别将半圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beae93062eb8d79570ec05eec3fda9ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/1392d841-3d2d-4c18-942d-f72f596c0f89.png?resizew=402)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/a3ab480c-a13e-4637-8c1d-3bb49307a35e.png?resizew=458)
交流:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b1672953164c806fee8e7d6d8336c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beae93062eb8d79570ec05eec3fda9ad.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/ab5272e3-17a6-48ba-b057-530a280b9903.png?resizew=517)
探究:你认为当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beae93062eb8d79570ec05eec3fda9ad.png)
(2)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0b9d36c7abf2b4735d7cbce6a16a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8e23cd691c52b5ad11efda042606dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/c62c5f38-4b06-456e-8af6-f83928ca4de2.png?resizew=167)
您最近一年使用:0次
2022-09-08更新
|
1542次组卷
|
3卷引用:2022年江苏省镇江市中考数学真题
解答题-作图题
|
困难(0.15)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/b90dafa2-298c-4bf9-bc86-ac5fd00859f5.png?resizew=402)
(1)【初步认识】
请用直尺和圆规在图①中作出面积最大的圆(不写作法,保留作图痕迹).
(2)【继续探索】
若三角形铁皮上有一破损的孔点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)【问题解决】
如图③,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eeb0c8df3d8c5260768c5e407b3583a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b939af5ba06e279cce39396aaf0fae06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
解答题-证明题
|
较难(0.4)
解决问题常常需要最近联想,迁移经验.例如研究线段成比例时需要想到……
(1)【积累经验】如图①,⊙O是△ABC的外接圆,AD是△ABC的高,AE是⊙O的直径.求证
.
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977735726678016/2979357538902016/STEM/0085767c-2d35-464f-b4f5-d02ff3e8de8c.png?resizew=179)
(2)如图②,已知线段a,b,c.用两种不同的方法作线段d,使得线段a,b,c,d满足
.要求:①用直尺和圆规作图;②保留作图的痕迹,写出必要的文字说明.
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977735726678016/2979357538902016/STEM/f6179579-fb6c-463c-8c91-086f3ba4f59f.png?resizew=406)
(3)【问题解决】如图③,已知线段a,b.AB是⊙O的弦.在⊙O上作点C,使得CA·CB=ab.要求:①用直尺和圆规作图;②保留作图的痕迹,写出必要的文字说明.
(1)【积累经验】如图①,⊙O是△ABC的外接圆,AD是△ABC的高,AE是⊙O的直径.求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab223b1963ebbe615ac614e0e9108ca.png)
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977735726678016/2979357538902016/STEM/0085767c-2d35-464f-b4f5-d02ff3e8de8c.png?resizew=179)
(2)如图②,已知线段a,b,c.用两种不同的方法作线段d,使得线段a,b,c,d满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df50f7ca6a558c16090f6fce5db81d0.png)
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977735726678016/2979357538902016/STEM/f6179579-fb6c-463c-8c91-086f3ba4f59f.png?resizew=406)
(3)【问题解决】如图③,已知线段a,b.AB是⊙O的弦.在⊙O上作点C,使得CA·CB=ab.要求:①用直尺和圆规作图;②保留作图的痕迹,写出必要的文字说明.
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977735726678016/2979357538902016/STEM/936e1d6f-7d1e-4b09-b76f-6d05a92625f4.png?resizew=385)
您最近一年使用:0次
解答题-问答题
|
较难(0.4)
“三等分角”是数学史上一个著名问题,数学家们证明只使用尺规无法三等分一个任意角,但对于特定度数的已知角,如
角、
角、
角等可以用尺规三等分,如果作图工具没有限制,将条件放宽,将任意角三等分是可以解决的.
(1)用尺规三等分特殊角.
例题解读:如图1,
,在边
上取一点
,用尺规以
为一边向
内部作等边
,作射线
,再用尺规作出
的平分线
,则射线
,
将
三等分.
![](https://img.xkw.com/dksih/QBM/2023/8/8/3298495989522432/3416733969743872/STEM/5223888a4c7e4f319ce6bb7dedf34d68.png?resizew=529)
问题1:如图2,
,请用尺规把
三等分.(不需写作法,但需保留作图痕迹)
(2)折纸三等分任意锐角.
步骤一:在正方形纸片上折出任意
,将正方形
对折,折痕记为
,再将矩形
对折,折痕记为
,得到图3;
步骤二:翻折正方形纸片使点
的对应点
在
上,点
的对应点
在
上,点
对折后的对应点记为
,折痕记为
,得到图4;
步骤三:折出射线
,
,得到图5,则射线
,
就是
的三等分线.
下面是证明射线
,
是
三等分线的部分过程.
证明:如图5,过点
作
,垂足为
,则四边形
为矩形.
根据折叠的性质,得
,
,
.
.
.
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
问题2:①将剩余部分的证明过程补充完整;
②若将图3中的点
与点
重合,重复(2)中的操作过程得到图6,请利用图6计算
的值,请直接写出结果.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ce270dc393605896e5b9d5f5ebebd0.png)
(1)用尺规三等分特殊角.
例题解读:如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0273bff68b222a6fddb7147ee367989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea7b811fa609b8e92da877471564e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://img.xkw.com/dksih/QBM/2023/8/8/3298495989522432/3416733969743872/STEM/5223888a4c7e4f319ce6bb7dedf34d68.png?resizew=529)
问题1:如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6b253b7f7aa120fa6dd980bfc5fabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
(2)折纸三等分任意锐角.
步骤一:在正方形纸片上折出任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1612d2cbcb5a1eb6b8f7cb261c79bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e825de4e5ade72e45a28c8f75b1dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
步骤二:翻折正方形纸片使点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
步骤三:折出射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1612d2cbcb5a1eb6b8f7cb261c79bd.png)
下面是证明射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1612d2cbcb5a1eb6b8f7cb261c79bd.png)
证明:如图5,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69a4829e972964e61abe6f79756b91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9369c27f58c821ef2b5816066b7c520.png)
根据折叠的性质,得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9fbef3c176da38c4d580325d265af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad02151a4064863424b3b15365dc4ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c9731b02df1913eca2a3bd0f702cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5915561ba96ff868d266b4fdf38c8e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c08cc40d7c3adb214aad6400775b48a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac522cc14ebab8d46c6a44b33926598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
问题2:①将剩余部分的证明过程补充完整;
②若将图3中的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd90c9ff8a48465550e329fbcbd46c6.png)
您最近一年使用:0次
解答题-作图题
|
较难(0.4)
“等弧”的探究.
【初步研究】
(1)如图①,
,
分别是
,
的弦,
,
,求证:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/864a00f7-96f0-43a7-a942-0edc33b654c8.png?resizew=490)
【深入研究】
(2)如图②,在
中,
,
是以A为圆心且与
相切的弧,在
的内部(包含边界)存在
,使
,且点M,
分别在边
,
上.
①在图②中,用直尺和圆规作出一条
(保留作图痕迹,写出必要的文字说明);
②若
,
,则满足条件的
所在圆的圆心轨迹的长度为_____.
【解决问题】
(3)如图③,折扇
完全打开后,
、
的夹角为
,
长为
,为了装饰折扇,现需从四边形丝绸材料
中剪出
,使
,且为了节约材料,
与边
,
均相切,已知
,
,
,请在图中用直尺和圆规作出满足条件的
.(保留作图痕迹,写出必要的文字说明)
【初步研究】
(1)如图①,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1ade05c093cea08d3eb211b2280a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86286109c71d2dd4be73dd7f1fcb67ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42b2dce8b04d5e32b72fa33324367fb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/864a00f7-96f0-43a7-a942-0edc33b654c8.png?resizew=490)
【深入研究】
(2)如图②,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1816fb0bed72025e79aa4b7185055ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c44512cb86bcf48c6d21357f45b533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae728c7be0f0cf78711f3fa5ccccf30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6a8b82726cba48302587ecb638be8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
①在图②中,用直尺和圆规作出一条
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4fea9fe2deb8cabf42601e5ef6df9d.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284a563413dc0532138fb2a64db8cc2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f83b02dc7659d7fdad5771da6996d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4fea9fe2deb8cabf42601e5ef6df9d.png)
【解决问题】
(3)如图③,折扇
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668a3f3ce5b8a272ad92c2ebd233f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6b11637ea396e989ab32d780e745b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59285ed2cfeafa81872b7be532a1ea81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6b11637ea396e989ab32d780e745b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e459e24a3c880c0aaa155e56a8dde9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691048ce61c91a8a3680fa3025193160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacd9f32e3dc2021c7d8bbae96622d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6b11637ea396e989ab32d780e745b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/4e6ad378-5a20-4b10-bf66-0b21645e744b.png?resizew=405)
您最近一年使用:0次
2023-12-17更新
|
188次组卷
|
3卷引用:江苏省南京市玄武区2023-2024学年九年级上学期期中数学试题
解答题-证明题
|
较难(0.4)
在等边三角形
中,点
分别边
上.
(1)如图1,若将等边三角形
沿
翻折,点
恰好落在边
上的点
处,
①求证:
;
②若
,若设
,求
与
的函数关系式及
的最值.
(2)尺规作图:在
边上求作一点
使
,(不写作法,保留作图痕迹,请在图2中找出所有符合条件的点
)
(3)若
,设
,若要使得(2)中只能作出唯一的点
,则
的值应该满足什么条件,请通过计算说明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d54431bbb28ebd98db5c1dc6083a75.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/fec8e38b-92ec-47a7-b65e-9ac0c6341384.png?resizew=363)
(1)如图1,若将等边三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684a0c147cc411b2c7f6bc71ee23102c.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfcabe92de0e6cabbbd9a3dc7910742c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01173d54eb2b5a6168d928feb0c51603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)尺规作图:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add60595ecea5d00ff1fbb2a5409be73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c142cedde260a13bb42b9c34fe98fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29927656edc488a91e9969d4ff43bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次