名校
解题方法
1 . 线段AB的长度为6,C,D为其三等分点(C靠近A,D靠近B),若P为线段AB外一点,且满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c99c33cf34fa55b63f78ad1acaccc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b0073fed28fd0caeade3216a5a5b2a.png)
A.36 | B.-36 | C.-8 | D.8 |
您最近一年使用:0次
2023-11-03更新
|
647次组卷
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4卷引用:江苏省徐州市普高联考(求实高中等)2023-2024学年高三上学期测评(三)数学试题
名校
2 . 定理:如图,已知P为
内一点,则有
.
已知点
在
内部,有以下四个推论:
①若
为
的重心,则
;
②若
为
的外心,则
;
③若
为
的内心,则
;备注:若
为
的内心,则
也对.
④若
为
的垂心,则
.
试用“奔驰定理”或其它方法解决下列问题.
(1)点
在
内部,满足
,求
的值;
(2)点
为
内一点,若
,设
,求实数
和
的值;
(3)用“奔驰定理”证明推论②.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a760158be533dc2e8656411ebf628ddb.png)
已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf0edea792798049cd728af69f74e19.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296b3c900b196c311f20b89dfa40cd83.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ece143a342b4f057a89818eee185a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76429bb17df7ee3fef82f2ce4301b6d2.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548011a81b29fc3b51b7f2bea99126e7.png)
试用“奔驰定理”或其它方法解决下列问题.
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62613718910c94b0542692291341e0ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba147c397c72a6d4f93ee2b4bbfe34.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb68c717f319b8b222ed7fccb73f8e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fcdec5fda440bbf42cf2472990e1e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
(3)用“奔驰定理”证明推论②.
您最近一年使用:0次
2022-04-13更新
|
1487次组卷
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4卷引用:江苏省徐州市第三十六中学2021-2022学年高一下学期第一次月考数学试题
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