1 . 已知圆O:
和圆C:
,圆心为点C,现给出如下结论,其中正确的个数是( )
①圆O与圆C有四条公切线
②过点C且在两坐标轴上截距相等的直线方程为
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
③过点C且与圆O相切的直线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b10208f5af532e9b621cf113c688e14.png)
④P、Q分别为圆O和圆C上的动点,则
的最大值为
,最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51e5a3a88f7d166f2877a5bc22a6bca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7acd2faeb5513785c3169d6b29dd1d.png)
①圆O与圆C有四条公切线
②过点C且在两坐标轴上截距相等的直线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d816a6e4a5c6375309040fdda0038b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
③过点C且与圆O相切的直线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b10208f5af532e9b621cf113c688e14.png)
④P、Q分别为圆O和圆C上的动点,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6612d35ed52e5e28da9ee4cba4fd5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51e5a3a88f7d166f2877a5bc22a6bca.png)
A.0 | B.1 | C.2 | D.3 |
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2 . 在平面直角坐标系中,矩形
,
,
,
,将矩形折叠,使
点落在线段
上,设折痕所在直线的斜率为
,则
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114460aab294eb99eec63e94b675216f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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3 . 如图,网格纸上的小正方形的边长均为1,粗线画的是一个几何体的三视图,则该几何体中最长的棱长为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/357af252-cd19-471f-b263-57097e658ab1.png?resizew=141)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/357af252-cd19-471f-b263-57097e658ab1.png?resizew=141)
A.![]() | B.4 |
C.![]() | D.![]() |
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4 . 如图,在长方体
中,
,
,异面直线
与
所成的角为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/f784d2b1-86fc-4239-8013-ade01a3ae6cd.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e45b0e1c3f6f5bc4cc81290bf263d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/f784d2b1-86fc-4239-8013-ade01a3ae6cd.png?resizew=170)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 某水平放置的平面图形的斜二侧直观图是等腰梯形(如图所示),将该平面图形绕其直角腰AB边旋转一周得到一个圆台,已知
,则该圆台的表面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/5ad11ee8-8afc-4d4e-b0aa-2136ffe17610.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db85a9f02f696b0013b0c0b629bc97bd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/5ad11ee8-8afc-4d4e-b0aa-2136ffe17610.png?resizew=170)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 已知
的顶点
,
边上的中线
所在直线的方程为
,
边上的高
所在直线的方程为
.
(1)求直线
的方程.
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6329198247b9c39bb31f0ce7e08f1f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b683c0866e725bd30dd41c31149635cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044cfca7b534fa44075ded7f1a6aa038.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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7 . 已知点
,若在坐标轴上存在一点
,使直线
的倾斜角为
,则点
的坐标不能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fadc9a19de13ca7688ca93f0c70a8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 若直线经过
,
两点,则直线
的倾斜角为()
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177ae4fa30cba0272d338973b8f7bdf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 直线
:
与圆
:
的位置关系是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d317ac4c21a49bbfca5280726f738b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfd4539423347f7844fbbfee06a777c.png)
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10 . 正四面体是棱长都相等的正三棱锥,若正四面体的棱长为2,则该正四面体的体积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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