名校
解题方法
1 . 已知三棱锥
,点
是
的外心.
(1)若
,求证:
;
(2)求点
到平面
距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20916a8a46d21b2b21f2b18321934bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/21/ea513005-d25e-4a41-8564-3a7ad9fe5bff.png?resizew=135)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f06685685376fe7fb30bf8d7e46575e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2023-07-17更新
|
217次组卷
|
2卷引用:福建省莆田市2022-2023学年高一下学期期末质量监测数学试题
名校
2 . 如图,在正三棱柱
中,
,
为
的中点,
、
在
上,
.
(1)试在直线
上确定点
,使得对于
上任一点
,恒有
平面
;(用文字描述点
位置的确定过程,并在图形上体现,但不要求写出证明过程)
(2)已知
在直线
上,满足对于
上任一点
,恒有
平面
,
为(1)中确定的点,试求当
的面积最大时,二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa40b456747f69437444833aab387be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.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/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2564f406fa222935e6d5bb24df0356a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/c34c1d0d-b0de-4ab5-8ff6-a1140bfc6c2c.png?resizew=127)
(1)试在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b17d7abbd564ce785f43a7c8526dc03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ef68c72248af27e3b83b4ee5fdeb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6b513ee7d966df71cd98b29ca4447e.png)
您最近一年使用:0次
2023-07-09更新
|
866次组卷
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6卷引用:福建省泉州市2022-2023学年高一下学期期末教学质量监测数学试题
福建省泉州市2022-2023学年高一下学期期末教学质量监测数学试题福建省永春第一中学2023-2024学年高一上学期8月月考数学试题福建省厦门市第一中学2023-2024学年高二上学期开学考试数学试题(已下线)10.4 平面与平面间的位置关系(第2课时)(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)专题04 立体几何初步(2)-【常考压轴题】(已下线)第二章 立体几何中的计算 专题一 空间角 微点10 二面角大小的计算综合训练【培优版】
名校
3 . 如图,在
中,
,点
在线段
上,过点
作
交
于点
,将
沿
折起到
的位置(点
与
重合),使得
.
平面
;
(2)试问:当点
在何处时,四棱锥
的侧面
的面积最大?并求此时四棱锥
的体积及直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37750daa8ba3b3fe3e9e2092f81c848.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bd9e8b54864ca44115d24a5aeeb83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47018187985efa84e161cc1a72ed4b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc97cc47a65c900c7ff295c5e7e576d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
(2)试问:当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212778bdc88a57d8c3a7015bc7432046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739ad948445af72d585fe29c745929b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212778bdc88a57d8c3a7015bc7432046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03952d664fba91020fc5f3bcf2f9746.png)
您最近一年使用:0次
名校
4 . 如图,四面体
中,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/1/2/2368530279997440/2369360141246464/STEM/a45ef089419b41248d5f29738b12bc94.png?resizew=220)
(1)证明:
;
(2)已知
是边长为2正三角形.
(Ⅰ)若
为棱
的中点,求
的大小;
(Ⅱ)若
为线段
上的点,且
,求四面体
的体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24914bb2ddc7a5d0cb8772ea5fd31401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ee4a6a3380d56e876c8bb7f04ef53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2020/1/2/2368530279997440/2369360141246464/STEM/a45ef089419b41248d5f29738b12bc94.png?resizew=220)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a97ec8912352afb1a702924163d75daf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bcdc38238794c82e7cd92fa4ab7af99.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60dc9f8e47e78b7f4ab2dd9cd559f601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe7222603916a937e6a59313cff475e.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60dc9f8e47e78b7f4ab2dd9cd559f601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207d35fbb2504a3e9f4aafdb80b7a96a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55bf39b6c78f5b45d8e5e908960e2cf5.png)
您最近一年使用:0次