名校
1 . 如图,
和
中,
,直线
与
交于点H.
时,延长
交直线
于点H,交
于点F,求
的度数(用含a的式子表示);
(2)当
时,将
绕点C旋转一周.
①如图2,当点E在直线
右侧时,求证:
;
②当
时,若
,请直接写出线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35fb1b056ac735cdc3d67f38500a6ada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f98c416e8485eda0c98c5fd67a0c47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b5ea2fc43b19ca043581eb94197234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33120cf053b12b204b49d2affa917922.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac762a2899a58faa0d3ab44f1281fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35fb1b056ac735cdc3d67f38500a6ada.png)
①如图2,当点E在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9312bbab2e10c4be8d53d75b7a48c977.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5da145dac12b560bb7cfb2529c596d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471d5febb0e752fc3387682311dc6117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
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2卷引用:福建省福州市第三十二中学2023-2024学年九年级下学期月考数学试题
2011·河北·中考模拟
名校
解题方法
2 . 如图1,点
分别是边长为
的等边
的边
上的动点,点
从顶点
,点
从顶点
同时出发,且它们的速度都为
.
交于点
,则在
运动的过程中,
变化吗?若变化,则说明理由;若不变,则求出它的度数;
(2)点
在运动过程中,设运动时间为
,当
为何值时,
为直角三角形?
(3)如图2,若点
在运动到终点后继续在射线
上运动,直线
交点为
,在
运动的过程中,
的大小变化吗?若变化请说明理由:若不变,请求出它的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3355e2fa0ac6c675f02ee36c3ced4f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9174c3b1324cf81098e42e0480bcc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddda95fe14d2476cd4c45905a8b2ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9baba5742fe32111ddd8a76fd5b265.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953b69a185ed4302f3d0e48bbbaa75f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c495b8fd7f7bb21c177c9d50fbf6919.png)
(3)如图2,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3355e2fa0ac6c675f02ee36c3ced4f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddda95fe14d2476cd4c45905a8b2ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9baba5742fe32111ddd8a76fd5b265.png)
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41卷引用:2017届河南省南阳市新野县新航中学九年级下学期结业考试数学试卷(试卷)
2017届河南省南阳市新野县新航中学九年级下学期结业考试数学试卷(试卷)(已下线)2011年河北省中考模拟试卷数学卷(已下线)2011年湖北省崇阳县城关中学中考模拟数学卷2015-2016学年江苏省南通八一中学八年级上学期第一次月考数学试卷【校级联考】江西省兴国县2018-2019学年八年级上学期第四次月考数学试题湖南省长沙市中雅培粹学校2019-2020年度八年级上学期9月月考数学试题河南省信阳市王店乡第二中学2019-2020学年八年级11月月考数学试题2019年江苏省宜兴中学中考数学模拟试题(已下线)【万唯原创】2018年河南省中考数学试题研究-河南试卷-河南重难题型研究解答题重难点突破题型7湖南省长沙市湘一芙蓉中学一中双语联考2020-2021学年八年级上学期11月月考数学试题四川省成都武侯外国语学校2019-2020学年八年级下学期6月月考数学试题江苏省徐州市鼓楼区树人初级中学2023-2024学年八年级上学期10月月考数学试题天津市天津经济技术开发区国际学校2023-2024学年八年级上学期月考数学试题江苏省无锡市锡山区港下中学2023-2024学年八年级上学期10月月考数学试题辽宁省营口市西市区实验中学2023-2024学年八年级上学期11月月考数学试题江西省抚州市临川区第五实验学校2023-2024学年八年级下学期月考数学试题2015-2016学年江苏省江阴市华士片八年级上学期期中考试数学试卷2015-2016学年江苏省宿豫区实验初中八年级上学期期中考试数学试卷2015-2016学年四川省绵阳市三台县八年级上学期期中调研数学试卷辽宁省鞍山二中2017-2018学年八年级(上)期中数学试卷2017-2018学年山东省临沂市蒙阴县八年级(上)期末数学试卷【校级联考】山东省临沭县2018-2019学年八年级上学期期中考试数学试题福建省福州市福州延安中学2018-2019学年八年级上学期期中数学试题江苏省南通市崇川区八一中学2019-2020学年八年级上学期期中数学试题河北省衡水市武邑县武邑镇中学2017-2018学年八年级上学期期末数学试题四川省宜宾市高县2019-2020学年八年级上学期期中数学试题湖北省荆州市江陵县2021-2022学年八年级上学期期末考试数学试题山东省烟台市龙口市(五四制)2022-2023学年七年级上学期期中数学试题(已下线)第一次月考难点特训(一)与全等综合有关的压轴题-【微专题】2022-2023学年八年级数学上册常考点微专题提分精练(人教版)广东省深圳市南山区太子湾学校2022-2023学年八年级上学期期中考试数学试题天津市河西区2022-2023学年八年级上学期期末考试数学试卷天津市益中学校2022-2023学年八年级上学期期末考试数学试卷重庆市荣昌区2022-2023学年八年级上学期期末数学试题(已下线)天津市河西区枫林路中学2022-2023学年八年级数学上学期期末测试卷江苏省南通市启东市长江中学2022-2023学年八年级上学期期末数学试题(已下线)专题03 等边三角形综合问题-【微专题】2022-2023学年八年级数学下册常考点微专题提分精练(北师大版)(已下线)专题04 含30度角的直角三角形-【微专题】2022-2023学年八年级数学下册常考点微专题提分精练(北师大版)(已下线)期末真题必刷压轴60题(18个考点专练)-2023-2024学年八年级数学上学期期末考点大串讲(人教版)广东省佛山市三水区2023-2024学年八年级下学期期中数学试题湖南省郴州市桂阳县蒙泉学校2023-2024学年八年级下学期期中数学试题(已下线)期末复习(压轴题50题22个考点)-2023-2024学年八年级数学下学期期末考点大串讲(北师大版)
3 . 如图,四边形
为正方形,点E为
上的定点,点F是射线
上的动点,连接
.将点F绕点A逆时针旋转
得到点H,连接
,过点
分别作
和
的垂线交于点G,射线
与射线
交于点P.
为正方形;
(2)点F在运动过程中,判断点P的位置是否发生变化?并说明理由;
(3)连接
,探究线段
的数量关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449870555f4df74edd28dc83f0383f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e27d700becd7569ab631bc3113646a.png)
(2)点F在运动过程中,判断点P的位置是否发生变化?并说明理由;
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6b3fa8c69a596136072482f756026a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e688fe1ef5e387cf3192d410744f91.png)
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2卷引用:福建省莆田市城厢区第三中学2023-2024学年九年级下学期月考数学试题
名校
4 . 如图,在正方形
中,E、F分别为
和
上的点,作
于M.
;
(2)在
上截取
,连接
,G为
中点,连接
,
.
①依题意补全图形;
②用等式表示线段
和
的数量关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590f5c235ef2d9cf1e12c2f346c076d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dccae658474d434fd8a12e8015f9616b.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bba25a314fb799efba2895cb1f1f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
①依题意补全图形;
②用等式表示线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb11667abcb2759f301391b9850352be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e883f81c66ceef54d2d0556a68ed585.png)
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3卷引用:北京市清华大学附属中学2023-2024学年九年级下学期月考数学试题
5 . 如图,
是
的直径,弦
与
相交于点E,
.
(2)求证:
;
(3)若
的半径为4,
,求
的长.
![](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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7f35738524dcb80969b063f8966b4d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11496dcfa927b88586f361832750e335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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名校
6 . 如图,直角
中,
,
,
,点
是边
上一点,将
绕点
顺时针旋转
到点
,则
长的最小值是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
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河南省郑州市东枫外国语学校2023-2024学年九年级上学期12月月考数学试题2023年江苏省扬州市仪征市一模数学试题(已下线)专题10 图形的对称、平移、旋转-学易金卷:2023年中考数学一模试题分项汇编(江苏专用)广东省佛山市顺德区大良街道2022-2023学年八年级下学期月考数学试题2023年河南省郑州外国语中学中考三模数学试题2023年河南省郑州市郑州高新技术产业开发区郑州外国语学校三模数学试题河南省洛阳市2023-2024学年九年级上学期期中数学试题河南省洛阳市洛龙区2023-2024学年九年级上学期期中数学试题2024年江苏省徐州市沛县第五中学中考数学一模模拟试题(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)(已下线)专题9.4 图形的旋转(题型分类拓展)-2023-2024学年八年级数学下册基础知识专项突破讲与练(苏科版)
7 . 如图,
是等边三角形,
为
的外接圆,点D在劣弧
上,连结
并在
上取点E,使得
,连结
.若
,
,则
的半径为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da52672888bf3b53935112a33b248caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df34369163e511f14028168cb0b21186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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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)
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名校
9 . 在
中,对角线交于点O,E是
上一点,且
,连结
,当
时,若
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db07c6ce6c8b0e96a3470c6a3491334.png)
_________ °,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20588e78744cdcf4bfa6212f9d381983.png)
_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1625cb560f6b29ee8e86f491970472c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c01fc21bc71fd6853a0f31377b929b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab958cc170c404e353b2d8d74568002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db07c6ce6c8b0e96a3470c6a3491334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e25aa5c204fa24897777ca194c253a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20588e78744cdcf4bfa6212f9d381983.png)
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2024-04-13更新
|
132次组卷
|
2卷引用:浙江省杭州市西湖区十三中教育集团(总校)2023-2024学年九年级下学期4月月考数学试题
10 . 如图1,矩形
顶点
的坐标为
,定点
的坐标为
,动点
从点
出发,以每秒2个单位长度的速度沿
轴的正方向匀速运动,动点
从点
出发,以每秒1个单位长度的速度沿
轴的负方向匀速运动,P、Q两点同时运动,相遇时停止,在运动过程中,以
为斜边在
轴上方作等腰直角三角形
.设运动时间为
秒.
___________时,
的边
经过点
,当
___________时,点
落在边
上;
(2)设
和矩形
重叠部分的面积为
,求
与
的函数关系式;
(3)如图2,过定点
作
,垂足为
,当
的顶点
落在矩形
的内部时,过点
作
轴、
轴的平行线,分别交
、
于点M、N,若
,直接写出
的值___________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97be988d7c7b4a9b7d5591c1f9774d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da665a09193daac29cc9704a4052fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08361173b096d18b33210a955e109f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)如图2,过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0e8708ac4b5be5691d11125b337b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4794cf7c57bdd4825d9e6615e2527a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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