如图,AB为⊙O的直径,C为
的中点,D为劣弧CB上一个动点(点D不与B,C重合),过D作⊙O的切线交AB延长线于点P,连接CD并延长交AB延长线于点Q,给出下列结论:①若CB
DP,则∠DAB=22.5°;②若PB=BD,则∠DPA=30°;③DP可能成为∠BDQ的平分线;④若⊙O的半径为1,则CD⋅CQ=AB;⑤0°<∠PDQ≤45°.其中正确结论的个数为( )
![](https://img.xkw.com/dksih/QBM/2022/9/28/3076133317591040/3077016998051840/STEM/5082dc96b3544c6496e8bf4297c6fcdc.png?resizew=247)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://img.xkw.com/dksih/QBM/2022/9/28/3076133317591040/3077016998051840/STEM/5082dc96b3544c6496e8bf4297c6fcdc.png?resizew=247)
A.5 | B.4 | C.3 | D.2 |
22-23九年级·全国·单元测试 查看更多[1]
(已下线)第二十四章 圆(B卷·学霸加练卷,难度★★★★★)-【单元测试】2022-2023学年九年级数学分层训练AB卷(人教版)
更新时间:2022-09-29 18:30:01
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【推荐1】如下图,
,
,
交
于
,在
内有一点
,要使得
最短,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/d28a24cb-54f5-4765-b3b1-a2c649a216b9.png?resizew=206)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5969d2c05955f48cd5b3b65629ad5151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.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://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9953cb8f83187c7d93a82bb899da3f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25efef47c08d758c2a1778220eb5723f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/d28a24cb-54f5-4765-b3b1-a2c649a216b9.png?resizew=206)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
【推荐2】如图,在菱形
中,
,
,
分别交
、
于点
、
,
,连结
,以下结论:①
;②点
到
的距离是
;③
与
的面积比为
;④
的面积为
,其中一定成立的个数为( )
![](https://img.xkw.com/dksih/QBM/2020/6/22/2490291701579776/2492836674846720/STEM/d2dc975880434bbdace1edef9bd56c57.png?resizew=201)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/0761165f1176f3a5fe4f7b052832316d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297cd2ccc8db7ee23569710035a73e94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1dcdac71e394e495d069f64e1f1ce9.png)
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【推荐1】等腰△ABC中,AB=AC,以腰AB为直径的圆O,与底边BC交于P,若圆O与腰AC的交点Q关于直线AP的对称点落在线段OA上(不与端点重合),则下列说法正确的是( )
A.∠BAC>60° | B.30°<∠ABC<60° |
C.BP>![]() | D.![]() ![]() |
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【推荐2】已知锐角
.如图(1)在射线
上取一点
,以点
为圆心,
长为半径作
,交射线
于点
.连接
;(2)分别以点
、
为圆心,
长为半径作弧,交
于点
、
;(3)连接
,
.根据以上作图过程及所作图形,下列结论中错误的是()
![](https://img.xkw.com/dksih/QBM/2020/10/9/2567261921468416/2567804684500992/STEM/9cb849454c3e49a486eae81e1deb38fe.png?resizew=208)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6b11637ea396e989ab32d780e745b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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![](https://img.xkw.com/dksih/QBM/2020/10/9/2567261921468416/2567804684500992/STEM/9cb849454c3e49a486eae81e1deb38fe.png?resizew=208)
A.![]() |
B.若![]() ![]() |
C.![]() |
D.点![]() ![]() ![]() |
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【推荐1】如图,▱ABCD的三个顶点A、B、D均在⊙O上,且对角线AC经过点O,BC与⊙O相切于点B,已知⊙O的半径为6,则▱ABCD的面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/7/5762dc94-4904-4b12-b6e0-0040363e0aeb.png?resizew=165)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/7/5762dc94-4904-4b12-b6e0-0040363e0aeb.png?resizew=165)
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【推荐2】如图,圆O的半径为3cm,B为圆O外一点,OB交圆O于A,AB=OA,动点P从点A出发,以πcm/s的速度在圆O上按逆时针方向运动一周回到点A立即停止.当点P运动的时间为( )秒时,BP与圆O相切.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/200ca8a2-15c7-47fc-ad56-172470ab67ac.png?resizew=176)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/200ca8a2-15c7-47fc-ad56-172470ab67ac.png?resizew=176)
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【推荐1】如图,矩形纸片
中,
,
.点E、G分别在
,
上,将
、
分别沿
、
翻折,点A的对称点为点F,点D的对称点为点H,当E、F、H、C四点在同一直线上时,连接
,则线段
长为( )
![](https://img.xkw.com/dksih/QBM/2021/5/12/2719385570099200/2719432119476224/STEM/7d5a36a2-7e52-4b68-b90f-b04b6080614a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://img.xkw.com/dksih/QBM/2021/5/12/2719385570099200/2719432119476224/STEM/7d5a36a2-7e52-4b68-b90f-b04b6080614a.png)
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【推荐2】如图,点
在线段
上,在
的同侧作等腰直角三角形
和等腰直角三角形
,使
,连结
,
,
与
,
分别交于点
,
,连结
,下列结论:①
;②
;③
.其中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/fced1432-23e8-4824-8196-26b9ad3fbb69.png?resizew=233)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766ae8acaddb28f8a5a55eff086fd976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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A.①②③ | B.① | C.①② | D.②③ |
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