1 . 如图,在正四棱柱中,
为
的中点,则
中点到平面
的距离为
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2 . 已知点
为直线
上的动点,平面内的动点
到两定点
,
的距离分别为
和
,且
,则点
和点
距离的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfabee203f841f2792a036c4bca54cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c9dcfd9f4c5298035870cb88a34169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc46f09a8c079e2916af98bb2f96f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f077fb4f73c2123538e19365d84748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b918aef3758d9e8f580ef52f07841515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3185e538b718098304ce17143f6e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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3 . 在平面直角坐标系中,某菱形的一组对边所在的直线方程为:
,
,另一组对边
,
.则下列命题正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5a0c210fb01fa67c6ae92975e82514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8419b91d1bd3c5823b2b66d90bed31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7aa84db6decf2856dc5ed208fa21d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93628c150ebb15e876cd89a1de16e0d.png)
A.![]() |
B.与![]() ![]() ![]() |
C.该菱形的四个顶点共圆 |
D.该菱形的面积为定值 |
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4 . 已知
,
,
为原点,则
的外接圆方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f3cd3027a533dd07220f161c958602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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5 . 已知圆
,弦
过定点
,则弦长
不可能的取值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
A.![]() | B.![]() | C.4 | D.![]() |
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6 . 已知
是空间中三条互不重合的直线,
是两个不重合的平面,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f682870aa63eea67a9f3133b3dabac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
A.![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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重庆市西南大学附中、重庆育才中学、万州中学拔尖强基联盟2024届高三下学期二月联合考试数学试题(已下线)热点6-1 线线、线面、面面的平行与垂直(6题型+满分技巧+限时检测)(已下线)第2套 复盘提升卷(模块二 2月开学)广东省广州市执信中学2024届高三下学期教学情况检测(一)数学试题
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7 . 在平面直角坐标系中,过直线
上任一点
作该直线的垂线
,
,线段
的中垂线与直线
交于点
.
(1)当
在直线
上运动时,求点
的轨迹
的方程;
(2)过
向圆
引两条切线,与轨迹
的另一个交点分别为
,
.
(i)证明:直线
与圆
也相切;
(ii)求
周长的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236a066876764d090523afe0ea734a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50154acc6ad77c6c777fffe3a08afb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2273ae1ee99cec9c1304323bc9ebf75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f817fa2d2a8c4e38191900ed7730c879.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/7f9e8449aad35c5d840a3395ea86df6d.png)
(i)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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8 . 某游乐园中有一座摩天轮.如图所示,摩天轮所在的平面与地面垂直,摩天轮为东西走向.地面上有一条北偏东为
的笔直公路,其中
.摩天轮近似为一个圆,其半径为
,圆心
到地面的距离为
,其最高点为
点正下方的地面
点与公路的距离为
.甲在摩天轮上,乙在公路上.(为了计算方便,甲乙两人的身高、摩天轮的座舱高度和公路宽度忽略不计)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/c50080be-44e3-4828-9bf3-8f8e58a640df.png?resizew=218)
(1)如图所示,甲位于摩天轮的
点处时,从甲看乙的最大俯角的正切值等于多少?
(2)当甲随着摩天轮转动时,从乙看甲的最大仰角的正切值等于多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbbc31960240afea742753b6a8dad6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4053cc2a31e9703bf80b62b5ea18c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c758c27bec97c234d1d818c40f3d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1d5a8cd34aff27b8ed21c977c3946f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d112c9693aa126c92bf1402a1f66bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/c50080be-44e3-4828-9bf3-8f8e58a640df.png?resizew=218)
(1)如图所示,甲位于摩天轮的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当甲随着摩天轮转动时,从乙看甲的最大仰角的正切值等于多少?
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9 . 已知圆
过点
和点
,圆心在直线
上.
(1)求圆
的方程,并写出圆心坐标和半径的值;
(2)若直线
经过点
,且
被圆
截得的弦长为4,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18e9b80fdeaa8bd3cf97b3c214448f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1282cc43ebf4b459832fec04d805989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f047e7ed44a3897ec79c6c6a0c641fcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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10 . 已知圆C的方程为
,则圆C的半径为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586631cf97f1d2a17f5c5b7601651ebf.png)
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