1 . 如图,在三棱锥
中,二面角
是直二面角,若
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fe532cad7a1f9279d58874aa4def00.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/e4547a4f-4675-47a8-8d6f-f512d8c04a8f.png?resizew=150)
(Ⅰ)求三棱锥
的体积;
(Ⅱ)求点
到
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b107b118778650bdc523229900256418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fe532cad7a1f9279d58874aa4def00.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/e4547a4f-4675-47a8-8d6f-f512d8c04a8f.png?resizew=150)
(Ⅰ)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
(Ⅱ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2020-02-20更新
|
339次组卷
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2卷引用:江西省泰和中学2021-2022学年高二上学期第一次段考数学(理)试题
2 . 如图,四棱锥
中,
底面
,且底面
为平行四边形,若
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/10/9/2567397881675776/2567968275431424/STEM/97f644e4cce74a04b179d2d939a8896e.png?resizew=258)
(1)求证:面
面
;
(2)若
,求点
到平面
的距离
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://img.xkw.com/dksih/QBM/2020/10/9/2567397881675776/2567968275431424/STEM/97f644e4cce74a04b179d2d939a8896e.png?resizew=258)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068e62c79ff7a527ff494db199d40b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
您最近一年使用:0次
2020-10-10更新
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1626次组卷
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16卷引用:江西省贵溪市实验中学2020-2021学年高二上学期第一次月考数学(理)试题
江西省贵溪市实验中学2020-2021学年高二上学期第一次月考数学(理)试题江西省贵溪市实验中学2020--2021学年高二12月月考文科数学试题广东省阳春市第一中学2019-2020学年高二上学期月考三数学试题湖北省黄冈市黄梅国际育才高级中学2018-2019学年高一下学期5月月考数学试题江西省鹰潭市2021届高三(上)模拟命题大赛数学(文科)试题安徽省蚌埠第三中学2020-2021学年高二上学期11月教学质量检测数学(文)试题上海市七宝中学2018-2019学年高三上学期摸底考试数学试题2017届上海市浦东新区高考三模数学试题2017届上海市浦东新区高三下学期5月练习数学试题2019届重庆市四川外语学院重庆第二外国语学校高考模拟(三诊)(文科)数学试题2020届陕西省西安中学高三第二次模拟数学(文)试题2020届辽宁省锦州市渤大附中、育明高中高三下学期开学摸底考试数学(文)试题(已下线)专题04 立体几何-2020年高三数学(文)3-4月模拟试题汇编(已下线)文科数学-6月大数据精选模拟卷01(新课标Ⅲ卷)(满分冲刺篇)上海市金山中学2021届高三上学期期中数学试题陕西省宝鸡市陈仓区2021届高三下学期第一次质量检测文科数学试题
名校
解题方法
3 . 如图,
是正方形,点
在以
为直径的半圆弧上(
不与
,
重合),
为线段
的中点,现将正方形
沿
折起,使得平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/8a924854-f88f-444e-b2a8-5b432dc835ec.png?resizew=226)
(1)证明:
平面
.
(2)若
,当三棱锥
的体积最大时,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/8a924854-f88f-444e-b2a8-5b432dc835ec.png?resizew=226)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b4e753ef119608188c46a50ec597e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b31fb036fa1bb4aa5edfd369f49b45b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb1e11713f9472725072c8c4e88e31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c54d01623f09f23103f03ba1135fc6a.png)
您最近一年使用:0次
2020-02-18更新
|
1572次组卷
|
10卷引用:江西省南昌市第二中学2019-2020学年高二下学期第一次月考数学(文)试题
江西省南昌市第二中学2019-2020学年高二下学期第一次月考数学(文)试题安徽省四校2020-2021学年高三上学期适应性测试文科数学试题2020届湖南省高三上学期期末统测数学(文)试题2020届高三2月第02期(考点07)(文科)-《新题速递·数学》2020届河南省新乡一中高三二模数学(文科)试题2020届吉林省白山市高三联考数学(文)试卷2020届河北省衡水二中高三下学期二模数学(文)试题2020届河北省衡水中学高三下学期二模数学(文)试题(已下线)专题04 立体几何——2020年高考真题和模拟题文科数学分项汇编(已下线)痛点13 立体几何中的最值、轨迹问题-2021年新高考数学一轮复习考点扫描
4 . 如图,在四棱锥P-ABCD中,PA⊥平面ABCD,△ABC是正三角形,AC与BD的交点为M,又PA=AB=4,AD=CD,∠CDA=120°,N是CD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/07b8ad15-3091-407d-8e77-be64c12f6214.png?resizew=162)
(1)求证:平面PMN⊥平面PAB;
(2)求点M到平面PBC的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/07b8ad15-3091-407d-8e77-be64c12f6214.png?resizew=162)
(1)求证:平面PMN⊥平面PAB;
(2)求点M到平面PBC的距离.
您最近一年使用:0次
2020-10-03更新
|
2447次组卷
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6卷引用:江西省丰城中学、上高二中2023届高三下学期2月联考数学(文)试题
江西省丰城中学、上高二中2023届高三下学期2月联考数学(文)试题陕西省西安市八校2018届高三上学期第一次联考数学(文)试题人教A版(2019) 必修第二册 过关斩将 第八章 立体几何初步 本章复习提升人教B版(2019) 必修第四册 过关斩将 第十一章 立体几何初步 本章复习提升(已下线)考点38 直线、平面垂直的判定与性质(考点专练)-备战2021年新高考数学一轮复习考点微专题北师大版 必修2 过关斩将 第一章 立体几何初步 本章复习提升
名校
5 . 如图,直三棱柱
中,
,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/04995d23-7b87-42b4-af22-6ed033682091.png?resizew=163)
(1)证明:
平面
;
(2)已知
与平面
所成的角为30°,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/04995d23-7b87-42b4-af22-6ed033682091.png?resizew=163)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319d234a0586478d4e73020d48b3a10.png)
您最近一年使用:0次
2020-05-13更新
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2759次组卷
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16卷引用:江西省宜春市上高县第二中学2019-2020学年高三上学期11月月考数学(理)试题
江西省宜春市上高县第二中学2019-2020学年高三上学期11月月考数学(理)试题四川省广安市广安中学2019-2020学年高二9月月考(文)数学试题黑龙江省鹤岗市第一中学2019-2020学年高三上学期10月月考数学(理)试题江西省吉安市2019-2020学年高三上学期期中数学(理)试题2020届河北省衡水中学高三年级上学期五调考试数学(理科)试题四川省棠湖中学2019-2020学年高三下学期第二次月考数学(理)试题甘肃省永昌县第一中学2020-2021学年高三上学期第一次月考数学理试题【市级联考】辽宁省丹东市2019届高三总复习质量测试(一)理科数学试题湖北省襄阳市2019-2020学年高二上学期期末数学试题2020届黑龙江省实验中学高三上学期期末考试数学(理)试题(已下线)专题01 平行、垂直问题的证明(第三篇)-备战2020年高考数学大题精做之解答题题型全覆盖山东济南市历城第二中学2019-2020学年高一下学期开学考试数学试题江苏省无锡市江阴市高级中学2019-2020学年高二下学期期中数学试题2020届河北省衡水中学高三高考考前密卷(一)数学(理)试题湖北省宜昌市天问高中2019-2020学年高二(下)开学数学试题人教B版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 1.2 空间向量在立体几何中的应用 1.2.4 二面角
6 . 如图,在三棱柱
中,侧面
是菱形,
,
是棱
的中点,
,
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/2020/3/27/2428136999288832/2428831724412928/STEM/7648d1bf-2ce4-4a60-9b56-6fee5f797583.png)
证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
若
,面
面
,求
到面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac4fb99967c46a3855bcf2885b448c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fc4fbd9390e2a5200920910abc63b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59da0269add3993c134f46169f213907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86814dbae9a5343d69bb4647900b3bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2221fe3118d6d55a78201f1c5296777c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3bd9abb95b0e96333873fc454e03a7.png)
![](https://img.xkw.com/dksih/QBM/2020/3/27/2428136999288832/2428831724412928/STEM/7648d1bf-2ce4-4a60-9b56-6fee5f797583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45224f7eac9d0cef64bf28d93e7721a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2013579652aa5f53d43080856f01c374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fc4fbd9390e2a5200920910abc63b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445cfd832967db6bbaa0a2ea311b4f0d.png)
您最近一年使用:0次
2020-03-27更新
|
993次组卷
|
2卷引用:江西省吉安市第一中学2021-2022学年高二10月第一次段考数学(理)试题
解题方法
7 . 如图,在四棱锥
中,
,
,
,且
,
.
![](https://img.xkw.com/dksih/QBM/2020/3/18/2422133807710208/2422983057113088/STEM/34494107f04d439aa5267764898d604d.png?resizew=200)
(1)证明:
面
;
(2)在
上是否存在点
,使
平面
,若存在,请计算
的值,若不存在,请说明理由;
(3)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0277ebb355020d31b59861842ca379ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://img.xkw.com/dksih/QBM/2020/3/18/2422133807710208/2422983057113088/STEM/34494107f04d439aa5267764898d604d.png?resizew=200)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced22fbe85d4a749c7b0b6bbae3ea3e7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8676b624f105072a3185911b25c912dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
您最近一年使用:0次
8 . 在棱长为1的正方体
中,
分别为棱
、
的中点,
为棱
上的一点,且
,则点
到平面
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380c0e6bb85f13a03c30e6f3831660fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
9 . 如图
,四边形
中,
是
的中点,
,
,
,
,将(图
)沿直线
折起,使
(如图
).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6ae528a3-ec8a-47ae-9fa1-a0dcc577d6c8.png?resizew=231)
(1)求证:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3bd7fcc7124307e9c33f98c53f2edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19fc9f894312e55c87a0d6737080e233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d5853c26657db448af610ac72cca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73d73869615fbaef5bf4fed0b2209c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6ae528a3-ec8a-47ae-9fa1-a0dcc577d6c8.png?resizew=231)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c51c25b65a37b676ae3c3b71c29f9b.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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