1 . 如图所示的几何体中,
为三棱柱,且
平面
,四边形
为平行四边形,
,
.
(1)若
,求证:
平面
;
(2)若
,
,二面角
的余弦值为
,求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2016/7/1/1572857765330944/1572857771720704/STEM/edd5ecfd6b734c19969eebb2244be837.png?resizew=176)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42b730d87bb95763a48c69f1b0329ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fe926770d2354e172dec02f5ce2efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8b7dbd627b58c8b75edb37a61a5e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d027be176d18651cfd30f5492789ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcecfc88e45465b7e2215a8557148da.png)
![](https://img.xkw.com/dksih/QBM/2016/7/1/1572857765330944/1572857771720704/STEM/edd5ecfd6b734c19969eebb2244be837.png?resizew=176)
您最近一年使用:0次
2 . 如图,
是
的直径,
、
是
上的两点,
,过点
作
的切线
交
的延长线于点
,连接
交
于点
.
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572747378835456/1572747385151488/STEM/e548c43d4f6845899dcb234cbac36908.png)
(1)求证:
;
(2)若
,试求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572747378835456/1572747385151488/STEM/0289c4d8cc684778a96a41646264135a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572747378835456/1572747385151488/STEM/1c7fbbd4084244ea8fdb170bd1afc05e.png)
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572747378835456/1572747385151488/STEM/e548c43d4f6845899dcb234cbac36908.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572747378835456/1572747385151488/STEM/7a34ad4469e34596b840d053944c7383.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572747378835456/1572747385151488/STEM/9b560874f2eb41a09d94ebb4bd220eec.png)
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572747378835456/1572747385151488/STEM/5d6f0231396045ed8d2daacb6b836fbb.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在直三棱柱
中,
平面
,其垂足
落在直线
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/27e03838-9ca2-4e91-9e58-8cc08c45e48c.png?resizew=149)
(Ⅰ)求证:
;
(Ⅱ)若
是线段
上一点,
,三棱锥
的体积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/27e03838-9ca2-4e91-9e58-8cc08c45e48c.png?resizew=149)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dec5aabef249f61d52166823dc053ff.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3b6b242150a876721ef23eb4954575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfd0130396557991f805067e94a43fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505abdb4631fe10cdcdde3dc3d6aad32.png)
您最近一年使用:0次
2016-12-04更新
|
2226次组卷
|
7卷引用:2015-2016学年重庆巴蜀中学高二下期中文科数学试卷
4 . 如图,
是直角三角形,
,以
为直径的圆
交
于点
,点
是
边的中点,连接
交圆
于点
.
![](https://img.xkw.com/dksih/QBM/2016/5/26/1572650359750656/1572650366214144/STEM/d4f0137ddfc8429f9ad5661d2c684392.png)
(1)求证:
、
、
、
四点共圆;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde6182c16084365446aac3c4475d808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2016/5/26/1572650359750656/1572650366214144/STEM/d4f0137ddfc8429f9ad5661d2c684392.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e72f41aab0537f5a08199c365ac641.png)
您最近一年使用:0次
解题方法
5 . 已知椭圆
与
轴的交点
(点A位于点
的上方),
为左焦点,原点
到直线
的距离为
.
(1)求椭圆
的离心率;
(2)设
,直线
与椭圆
交于不同的两点
,求证:直线
与直线
的交点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cba824597ac1256ef641fb87346dda6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1936b35d7998bbae3f299c4e42fb76.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65920f4695a14c85e7085450aee08b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
6 . 如图,
的半径
垂直于直径
,
为
上一点,
的延长线交
于
,过
点的切线交
的延长线于
.
![](https://img.xkw.com/dksih/QBM/2016/3/29/1572564234248192/1572564240654336/STEM/6bb71137493d408d80a91b052e97df4b.png)
(1)求证:
;
(2)若
的半径为
,
,求:
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2016/3/29/1572564234248192/1572564240654336/STEM/6bb71137493d408d80a91b052e97df4b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6943b84a674fa270b62b0e687821fddd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bf432e4a457e8b3eecfcf131fec0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
解题方法
7 . 已知椭圆
的右焦点为
,点
在椭圆上.
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470766108672/1572470771818496/STEM/ceda92aa65fa4f249e1c241c2a05df10.png?resizew=229)
(1)求椭圆的方程;
(2)点
在圆
上,且
在第一象限,过
作圆
的切线交椭圆于
两点,求证:
的周长是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327126f348c456f0c628a2f57648ecea.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470766108672/1572470771818496/STEM/ceda92aa65fa4f249e1c241c2a05df10.png?resizew=229)
(1)求椭圆的方程;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50667ce76318b23b69ac6b8e16dc80d0.png)
您最近一年使用:0次
8 . 如图,在四棱锥
中,平面
⊥平面
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470766108672/1572470771671040/STEM/71a5a078acdd4ddd89f5bd56b0d9a540.png)
求证:(1)直线
∥平面
;
(2)直线
⊥平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6153163fecdf3f410411048428ccaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754ca3dea7da1b3ffd8ad899d8f6acc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f492dc0d98248c34366d1705c965fe6.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470766108672/1572470771671040/STEM/71a5a078acdd4ddd89f5bd56b0d9a540.png)
求证:(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)直线
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470766108672/1572470771671040/STEM/118a8d3ed72d44d98aaf9cb8deaaf226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
解题方法
9 . 已知椭圆
的离心率为
,左右焦点分别是
,
,点
为椭圆
上任意一点,且
面积最大值为
.
(1)求椭圆
的方程;
(2)过
作垂直于
轴的直线
交椭圆于
,
两点(点
在第一象限),
,
是椭圆上位于直线
两侧的动点,若
,求证:直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff4be53718fe6be96194eb4fdb04a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f2b7a031dac6fa9b22a23d8de02084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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10 . 设等差数列
的前
项和为
,
,
.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404d10711dae28deac242102c0c05e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9dc08571a7c9a77dc85cad5b578942.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74eca24376d4c4fd6181639d3eb63f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e06b0fda8954c395f1a3ccfbc88698.png)
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