1 . 到一个三角形的三个顶点的距离的平方和最小的点,是这个三角形的( ).
A.垂心 | B.重心 | C.外心 | D.内心 |
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2 . 在
中,已知
.如图所示,
是边
的垂直平分线上一点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564894aaa07d3110e0260dbc08a2f135.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51c70ed26bb56ec506175e6c9879e0b.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/564894aaa07d3110e0260dbc08a2f135.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/e8fdc98e-0cd7-48da-b017-7f85d9fae658.png?resizew=151)
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3 . 在正四面体
中,设
,
,记
和
所成的角为
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e888ea14da893971e13858945bf0cd.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932db76e7fb350bf0d1510c13aa4c958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62f5468b028f15b29edc20e7373939b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041b02bedb8c70bffccaa4b563312590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3415429304cf6733cd7bd5d9927af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e888ea14da893971e13858945bf0cd.png)
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名校
4 . 设正
的边长为1,
为任意的实数.则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143a76566c8e0904f4f82c61051264a7.png)
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5 . 如图,已知
是
的重心,若
过点
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a3693fc5a31e00178ee0fa74bab066.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12cfce6bedc9e8962a4a8b9afce4d4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c6970aac105dae55a5d4ad796c1ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a3693fc5a31e00178ee0fa74bab066.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/db17af90-ecfa-4456-86b3-272ea7d632af.png?resizew=165)
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6 . 设
为
所在平面内一动点.则使得
取得最小值的点
是
的( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9178fc8b5d65aa75fa9196294a0db7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0984f9c6ce16e60573a95841cc97a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9178fc8b5d65aa75fa9196294a0db7e.png)
A.外心 | B.内心 | C.重心 | D.垂心 |
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2018-12-27更新
|
466次组卷
|
2卷引用:数学奥林匹克高中训练题_114
7 . 四面体
中,
面
,
,点
满足
,其中,
、
、
为正数且
.若直线
是由到面
、面
和面
的距离相等的点构成,则二面角
的余弦值为(用
、
、
表示)______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb554b9fec080a9e261619e615b4c176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cb0226499bf24041f4f6c866a9bb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb802b0cd77d772dceff0d9ff6c879ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c317f156ce7a6fa94256d72ce0dcb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de908dd52536dc51de6e71920c847d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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8 . 如图,在
的边上做匀速运动的三个点
、
、
,当
时,分别从
、
、
出发,当
时,恰好同时到达
、
、
.那么,这个运动过程中的定点是
的( )
![](https://img.xkw.com/dksih/QBM/2018/12/21/2101630772740096/2105615210512384/STEM/635a2713e4b1448e91e83ed202e9dd58.png?resizew=193)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b12eb17187b2bdb6246b477274e4b34.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14effb5263b6b8ed7748f05586177a63.png)
![](https://img.xkw.com/dksih/QBM/2018/12/21/2101630772740096/2105615210512384/STEM/635a2713e4b1448e91e83ed202e9dd58.png?resizew=193)
A.内心 | B.外心 |
C.垂心 | D.重心 |
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2011高三·辽宁·竞赛
9 . 已知直线
与抛物线
交于
、
两点(点
在
轴上方),与
轴交于点
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067567d99cf3430de131088249e5915e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4bdbef22c617288a80b656551e6370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b98930a5300353f62d889df70c1b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067567d99cf3430de131088249e5915e.png)
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