定义:三角形一个内角的平分线和与另一个内角相邻的外角平分线相交所成的锐角称为该三角形第三个内角的遥望角.
(1)如图1,∠E是△ABC中∠A的遥望角,若∠A=α,请用含α的代数式表示∠E.
(2)如图2,四边形ABCD内接于⊙O,
=
,四边形ABCD的外角平分线DF交⊙O于点F,连结BF并延长交CD的延长线于点E.求证:∠BEC是△ABC中∠BAC的遥望角.
(3)如图3,在(2)的条件下,连结AE,AF,若AC是⊙O的直径.
①求∠AED的度数;
②若AB=8,CD=5,求△DEF的面积.
(1)如图1,∠E是△ABC中∠A的遥望角,若∠A=α,请用含α的代数式表示∠E.
(2)如图2,四边形ABCD内接于⊙O,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87ab63321823962564a03fa9a5765dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d887dec04b7d49d19ad65ef5db3598e.png)
(3)如图3,在(2)的条件下,连结AE,AF,若AC是⊙O的直径.
①求∠AED的度数;
②若AB=8,CD=5,求△DEF的面积.
2020·浙江宁波·中考真题 查看更多[12]
浙江省宁波市2020年中考数学试题山东省济宁市兖州区2020-2021学年九年级上学期期末数学试题2021年江苏省盐城市阜宁县中考数学一调试题2021年江西省赣州市石城县中考数学第一次联考试卷 江苏省盐城市阜宁县2020-2021学年九年级下学期第一次学情调研数学试题2020年浙江省诸暨中学九年级中考提前招生选拔考试数学试题(已下线)专题14 圆压轴题型汇总-三年(2020-2022)中考数学真题分项汇编(浙江专用)2023年山东省泰安市东平县中考三模数学试题2024年浙江省温州市中考数学一模考前模拟试题2023年山东省泰安市东平县三模数学模拟预测题2024年浙江省嘉兴市九年级学业水平考试数学模拟预测题2024年浙江省杭州市中考数学三模练习试题
更新时间:2020-07-04 07:38:35
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解答题-问答题
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【推荐1】如图,直线
的函数表达式为
,与
轴交于点A,直线
经过点
和点
,且直线
交于点
.
(1)求点A,点
的坐标;
(2)点
是
轴上的一个动点,求
的最小值;
(3)点
分别是直线
上的两点,且不与点
重合. 当
时,直接写出每一组点
和点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16f97c8aada9ec7265f4e887f917c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f605a7fc2f1064fe14882ee426839db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a1a843e25ebb752cea96f28ef5c0eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/26/9117bec6-696d-4cf5-8a30-54bf94a59257.png?resizew=161)
(1)求点A,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1e1daca79300596c9a8d37b5cb6b18.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bdfb1fd180087921a75afb46d3de436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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【推荐2】如图,在
和
中,
,
,
,连接
、
,
与
相交于点
、交
于
,
与
相交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/8df5ebc2-7c9f-4547-93d6-5bd259302193.png?resizew=191)
(1)求证:
;
(2)求证:
;
(3)连接
,
,有以下三个结论:①
平分
;②MC平分
;③
.
其中正确的有__________,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78c42618c038aa8bf15cb6151d3209b.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ead706ccc238d868654030a3626847c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/8df5ebc2-7c9f-4547-93d6-5bd259302193.png?resizew=191)
(1)求证:
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(2)求证:
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(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e883f81c66ceef54d2d0556a68ed585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8985044e087fe47e932dcae22730828b.png)
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其中正确的有__________,请说明理由.
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名校
【推荐1】如图,在
中,
,以
为直径的
交
于点
,点
为
延长线上一点,延长
交
于点
,连接
,
.
(1)求证:
是
的切线;
(2)若
,
时,求
的长.
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/14/1e556277-b552-465d-a008-c3b603b13362.png?resizew=141)
(1)求证:
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(2)若
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解答题-作图题
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较难
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【推荐2】如图,在
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/b74c6e8c-1346-42fd-900e-ea43f0aad207.png?resizew=219)
(1)利用尺规作
,使
经过点
和点
,圆心
在线段
上,该圆与
的另一交点为
(保留作图痕迹,不写作法).
(2)在(1)条件下,求
;
(3)设
是线段
上任意一点(不与
,
重合),连接
,当
的最小值为
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02adb59f0d7889cb04237104445c5766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb01d2b57580731c8b807ac8cffc8ba.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/b74c6e8c-1346-42fd-900e-ea43f0aad207.png?resizew=219)
(1)利用尺规作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
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(2)在(1)条件下,求
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(3)设
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.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/8c406c4f1880daebcccf913ba3f93512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2b4b75616fce7d4e8c225598c4f9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e78c013cb4fc61193b651072d5e15de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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【推荐1】如图,在
中,
,
,点
在
延长线上,点
在
上,且
,延长
交
于点
,连接
、
.
![](https://img.xkw.com/dksih/QBM/2020/4/5/2435072055115776/2435894439550976/STEM/ac716819-d4be-422c-b4b9-73243879b5b5.png)
(1)求证:
;
(2)若
,则
__________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4908fad3dc6fe1b0675c870328f043ef.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://img.xkw.com/dksih/QBM/2020/4/5/2435072055115776/2435894439550976/STEM/ac716819-d4be-422c-b4b9-73243879b5b5.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d96a5d40d0aea9f4398ca4d0fe9b0dd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40113c5e2b3869561c001d71e090b46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292029a209c653d03fa8a53daf4f7d89.png)
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真题
【推荐2】如图,已知⊙O是△ABC的外接圆,且BC为⊙O的直径,在劣弧
上取一点D,使
,将△ADC沿AD对折,得到△ADE,连接CE.
(1)求证:CE是⊙O的切线;
(2)若CE
C D,劣弧
的弧长为π,求⊙O的半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfae24e2f0f495d0c742c7bfcffc5eae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24eba28ce24b1742dee7e47e83ffcfdc.png)
(1)求证:CE是⊙O的切线;
(2)若CE
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e589def3e7fe21b601bc6d5144073202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445f118e9cf8cf1dac2351305ea0ba4b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/18/d736d804-5058-44df-ba45-7f1b187be2aa.png?resizew=158)
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【推荐3】问题提出
苏科版《数学》九年级(上册)习题2.1有这样一道练习题:
![](https://img.xkw.com/dksih/QBM/2017/11/20/1821119757213696/1823244111945728/STEM/fcb7bfb76610414ebabd13bbbeb3b107.png?resizew=192)
在解决此题时,若想要说明“点B、C、D、E在以点M为圆心的同一个圆上”只需证明 .
初步思考
如图②,BD、CE是锐角△ABC的高,连接DE.
求证:∠ADE=∠ABC.
小敏在解答此题时,利用了“圆的内接四边形的对角互补”进行证明.
(请你在下面的空白处根据小敏的思路完成证明过程.)
![](https://img.xkw.com/dksih/QBM/2017/11/20/1821119757213696/1823244111945728/STEM/2c25f2e62e254650a3eddd8dbf1c8be3.png?resizew=459)
推广运用
如图③,BD、CE、AF是锐角△ABC的高,连接DE、EF、FD.猜想∠EFB与∠DFC之间存在的关系,并说明理由.
苏科版《数学》九年级(上册)习题2.1有这样一道练习题:
![](https://img.xkw.com/dksih/QBM/2017/11/20/1821119757213696/1823244111945728/STEM/fcb7bfb76610414ebabd13bbbeb3b107.png?resizew=192)
在解决此题时,若想要说明“点B、C、D、E在以点M为圆心的同一个圆上”只需证明 .
初步思考
如图②,BD、CE是锐角△ABC的高,连接DE.
求证:∠ADE=∠ABC.
小敏在解答此题时,利用了“圆的内接四边形的对角互补”进行证明.
(请你在下面的空白处根据小敏的思路完成证明过程.)
![](https://img.xkw.com/dksih/QBM/2017/11/20/1821119757213696/1823244111945728/STEM/2c25f2e62e254650a3eddd8dbf1c8be3.png?resizew=459)
推广运用
如图③,BD、CE、AF是锐角△ABC的高,连接DE、EF、FD.猜想∠EFB与∠DFC之间存在的关系,并说明理由.
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|
较难
(0.4)
【推荐1】如图,点A是x轴非负半轴上的动点,点B坐标为(0,4),M是线段AB的中点,将点M绕点A顺时针方向旋转90°得到点C,过点C作x轴的垂线,垂足为F,过点B作y轴的垂线与直线CF相交于点E,连接AC,BC,设点A的横坐标为t.
(Ⅰ)当t=2时,求点M的坐标;
(Ⅱ)设ABCE的面积为S,当点C在线段EF上时,求S与t之间的函数关系式,并写出自变量t的取值范围;
(Ⅲ)当t为何值时,BC+CA取得最小值.
(Ⅰ)当t=2时,求点M的坐标;
(Ⅱ)设ABCE的面积为S,当点C在线段EF上时,求S与t之间的函数关系式,并写出自变量t的取值范围;
(Ⅲ)当t为何值时,BC+CA取得最小值.
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925238675423232/1925366380929024/STEM/74b32e2183b444929cf83735512889b6.png?resizew=249)
您最近一年使用:0次
【推荐2】如图1,直线
与y轴相交于点A,抛物线
也经过点A,其顶点为B.将该抛物线沿直线l平移使顶点B落在直线l上的点D处,点D的横坐标为
.
(1)求点B坐标;
(2)求平移后的抛物线
的解析式(用含n的式子表示);
(3)若平移后的抛物线
与原抛物线
相交于点C,且点C的横坐标为a.
①请求出a关于n的函数关系式;
②如图2,连接
、
,若
,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1794ac1aa451cda13537d610a2268bba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1ddb40139813c6fdf9eb148f24f6da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5e5ba3a62f61ff22319d3decfdc48b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/7e830cb5-7885-454f-a131-26bd042ddf1f.png?resizew=327)
(1)求点B坐标;
(2)求平移后的抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd49bf20f987c05b4d36e31549075c.png)
(3)若平移后的抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd49bf20f987c05b4d36e31549075c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
①请求出a关于n的函数关系式;
②如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d69c69c46ac34f560546c22af120be.png)
您最近一年使用:0次