真题
1 . 如图,
是等腰直角三角形,
,
,点
,
分别在
,
边上运动,连结
,
交于点
,且始终满足
,则下列结论:①
;②
;③
面积的最大值是
;④
的最小值是
.其中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9555c33c74280dcf9be3958e12a2109f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339b2711bee0b6bf5a04a48226786c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d49bc5b38319e3c2c48889e6b1fcff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b61b7416bc7deb40caca231375213b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36852ef951ef72606e4032f4e4881f48.png)
A.①③ | B.①②④ | C.②③④ | D.①②③④ |
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2 . “启智”数学兴趣小组对图形的旋转展开进一步探究,总结了一些方法和规律,请你完成相关问题.(画图工具不限,不写画法)
(1)动中有定:
如图1,
是边长为
的等边三角形.
①将点
绕点
顺时针旋转一周,点
的对应点为点
,请在图1中画出点
的运动路径,当点
不与A、B重合时,可得
__________
或__________
;
②将边
绕点
顺时针旋转一周,请在图1中画出线段
扫过的区域(用阴影表示,画出必要的辅助线),并求出该区域的面积.
(2)以静制动:
如图2,
中,
,
,将
绕点
旋转得
,点P是线段
上一个动点,点M是
的中点.
①线段
的最小值是__________,最大值是__________;
②点P到直线
的距离为h,当
时,求h的取值范围.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/bcc99d52-076a-4e0c-8b92-8956911c9f43.png?resizew=324)
(1)动中有定:
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
①将点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c96a4e6263a9d076a6fdee343f4371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
②将边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)以静制动:
如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8817091d0f4b7d7ac6df560cb63c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b185184dc2dc3894a0313fd13f26a59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
①线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
②点P到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c383691e8d740830a865b12d66f7633.png)
您最近一年使用:0次
名校
3 . 问题提出
(1)如图①,
的半径为4,圆心O到直线l的距离为6,则圆上一动点P到直线l的距离的最大值为______,最小值为______.
问题探究
(2)如图②,已知
,若
,求
的长.
问题解决
(3)如图③,在四边形
中,
,E为
的中点,
且
.在四边形内部存在一点P使得
,连接
,将
绕点B逆时针旋转
至
,连接
,问是否存在F使得
的面积最大?若存在,请求出
面积的最大值;若不存在,请说明理由.
(1)如图①,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
问题探究
(2)如图②,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3761d166d3fba7370189812bc90b431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d625c450c03d20451028d887fd5d8bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
问题解决
(3)如图③,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448ad48b1fdeb5da3497de05b44602b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b173ac8cc4ac4f1c9e1daaa605fbb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a1bf64ba772922fe58b5322eb4bced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6699ab8ef5ac674271983738e6b522b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df7626240940eb340420a605e95aeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df7626240940eb340420a605e95aeee.png)
您最近一年使用:0次
2024-01-08更新
|
109次组卷
|
2卷引用:江西省宜春市丰城中学2023-2024学年九年级下学期月考数学摸底试题
4 . 已知
为
轴正半轴上一点,
交
轴于
,
两点,交
轴于
,
两点,
点为劣弧
上一个动点(点
不与
,
重合),且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579cb273becd3fb9ec983a71cc8d9ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
,连接
,取
的中点
,连接
,
,则
与
具有怎样的关系?并求
的最大值;
(2)如图2,连接
,
,
,其中
与
轴交于点
,
平分
交
于点
;
①求点
的运动路径长;
②记
,
,求
关于
的函数关系式;
(3)如图3,连接
,
,
,求证:
定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5ab74296abcbcf994c02b5834cd699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/d053b14c8588eee2acbbe44fc37a6886.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579cb273becd3fb9ec983a71cc8d9ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c51486490ea53d773a76da9fda285b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48943db264c08adaf6ae0766fd56459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c51486490ea53d773a76da9fda285b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48943db264c08adaf6ae0766fd56459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c51486490ea53d773a76da9fda285b.png)
(2)如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfaca9396f85c0137b534903321fcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3730e2fa70360e60286cff11b37c3051.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d221944148d71e2e1bc76040aefb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b49fb2e0b62d51db4247496553a0ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ff0a6113c45cbf1bba72ebba589a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)如图3,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365822bd3945e6a3e871ca979c84cc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf8c7485b305ac3be306d78c9d3156e.png)
您最近一年使用:0次
名校
5 . 如图,矩形
中,
,
,点
,
分别为边
,
上的点,将线段
绕点
顺时针旋转
,得到线段
.射线
与对角线
交于点
,连接
,
.
的度数:
(2)若
,求
的值;
(3)连接
,
,若
,设
和
的面积分别为
,
,当点
在边
上运动时,求
的最大值及此时
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.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/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad1b0a76a887783392268ae203ad22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87448e09eaa816e50ae92d111d5ded6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87448e09eaa816e50ae92d111d5ded6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f30cb81835298cb612a828f355060a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8b62dc033d86ee9e561b8903796701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44403932b363682bafde45ca331506a4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01daf31fca84f592bdf2a8c25828eeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754c23a406ae64fcbfcd2ce7615d274a.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb11667abcb2759f301391b9850352be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935ad59079c158ea0f92018fc548e4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20462a7fe0d6eaac6eab00f56760418a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaecf08a22124a457128fb04c9c02bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
您最近一年使用:0次
6 . 如图,矩形
中,
,
,点E,F分别为边
,
上的点,将线段
绕点
顺时针旋转
,得到线段
.射线
与对角线
交于点
,连接
,
.
的度数;
(2)若
,求
的值;
(3)连接
,
,若
,设
和
的面积分别为
,
,当点
在边
上运动时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83cb6327dcbc8a998e6586bcfa7a3b9.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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44403932b363682bafde45ca331506a4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01daf31fca84f592bdf2a8c25828eeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754c23a406ae64fcbfcd2ce7615d274a.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20462a7fe0d6eaac6eab00f56760418a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaecf08a22124a457128fb04c9c02bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.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/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
名校
7 . 阅读材料:如图(1),在
中,
,点P在
边上,
于点
于点F,则
.(此结论不必证明,可直接应用)
如图(2),正方形
的边长为2,对角线
相交于点O,点P在
边上,
于点
于点F,则
______;
(2)【类比与推理】
如图(3),矩形
的对角线
相交于点
点P在
边上,
交
于点E,
交
于点F,求
的值;
(3)【拓展与延伸】
四边形
是半径为4的圆内接四边形,对角线
相交于点O,
,点P在弦
上,
交BD于点E,
交
于点F,当
时,试判断
的值是否为定值,若是请求出该定值并求出四边形
面积的最大值;若不是定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1336496362282a03b805c4d14b823308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b37625595a63cb47e1cdf9c5da40c3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff6927b60a532649f330cdecf5bf04a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0bfd5c0506342a0127b9d0a1ed9601.png)
如图(2),正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d578394cd8e4d7a705599269c512960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b37625595a63cb47e1cdf9c5da40c3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff6927b60a532649f330cdecf5bf04a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1c2a266873044e21dd02c9f7e4e0e0.png)
(2)【类比与推理】
如图(3),矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d578394cd8e4d7a705599269c512960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32ff7566dfbf1d22bf693f825d83ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7681c103bfed97988a516065d1c7d91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb754e9542819c137b4c049c5cff66aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bce17597a7a6a83cd4287d424db6b56.png)
(3)【拓展与延伸】
四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d578394cd8e4d7a705599269c512960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46cc1c481e243ca311a6369c8313a18f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d60f55c585f1b455027202684b13e7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2103beb858805577d9402209c518828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bce17597a7a6a83cd4287d424db6b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11c4cfb55d68dfc47530b4604f63d69c.png)
您最近一年使用:0次
8 . 【问题背景】小初同学在学习圆周角时了解到:圆内接四边形的对角互补.
如图①,点
、
、
、
均为
上的点,
,则有
______°;
【问题探究】爱思考的小初同学发现:如图②,点
,
,
,
均为
上的点,若
,点
为弧
上任意一点(点
不与点
、
重合),若点
在运动的过程中始终保持
,则
的度数恒为
.
下面是小初的证明过程:
证明:延长
至点使
,连接
.
缺失(1)
在
与
中,
,
∴
.
∴
,
,
,
又
,
∴
,
∴
,
∴
为等边三角形.
缺失(2)
请你补全缺失的证明过程.
【结论应用】如图③,点
,
,
,
均为
上的点,若
,点
为弧
上任意一点(点
不与点
、
重合),且
,
的半径为2,当点
在运动的过程中,四边形
的周长的最大值为______.
如图①,点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971186a68d48dbb81b3ca1f2a0ec0f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db90c0feb35aa54464f1303be9118f37.png)
【问题探究】爱思考的小初同学发现:如图②,点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/5963abe8f421bd99a2aaa94831a951e9.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/5bc93442cc086b44fc67907aac067d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
下面是小初的证明过程:
证明:延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a3a922f7ea64083c415c72259179a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
缺失(1)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c625a55ef1d2920a0605d52c8da23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c941cb13f64020851fd09e0514f2502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573ec93f55c65529008897713a65539.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b28d708b000067e25f3df570eb2a92.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ac49caae8e3b8869d19beeff98966e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a3a922f7ea64083c415c72259179a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce956bc96a1eb7bae2ad10879fbaeee.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc93442cc086b44fc67907aac067d3c.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5144f280c283f799ae4e51192cdfc38.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf4006da017dfa3f699c39ad0a24fbb.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b59f79992d67ee52d205537728f2745.png)
缺失(2)
请你补全缺失的证明过程.
【结论应用】如图③,点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc0b376ea9c9e8f28c6c03b83d9467b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
9 . 我们定义:有一组对角相等的四边形叫做“等对角四边形”.
内接于
,点
在
的延长线上,且
.证明:四边形
是“等对角四边形”.
(2)如图②,在
中,
,
,
,
平分
,点
在线段
上,以点
、
、
、
为顶点构成的四边形为“等对角四边形”,求线段
的长.
(3)如图③,在
中,
,
,
,若四边形
是“等对角四边形”,且
,则
的最大值是______.(直接写出结果)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30e50e094cd2849e38859b36aad0b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164e1cc74e41a2a55d3767c006392bfd.png)
(2)如图②,在
![](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/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
(3)如图③,在
![](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/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779a94ce085ee3dbde9581edd75ecb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f4793c8fd5918ed9d20c19f5bfc269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db7ea03277f8408fabe5b327cc34838f.png)
您最近一年使用:0次
10 . 如图,
是
的直径,点E在
上,
垂足为C,
点G在
上运动(不与E重合),点F为
的中点,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f913298f0fae9f55377a8deab9f099dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881cd6f6cc6df1e11d12a6726ddc476f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f3956f008cc29ca4bae44a087d5427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
A.![]() | B.6 | C.![]() | D.8 |
您最近一年使用:0次