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zhi dian fa qian tan
Author(s): ZHU Jingyuan
Pages: 17-
19
Year: 2016
Issue:
5
Journal: High-School Mathematics
Abstract: 1 质点法简介
先从一个简单的题目开始谈起.
例1 如图1,四边形ABCD内接于圆,△BCD、△ACD、△ABD、△ABC的垂心分别为H1 、H2、H3、H4.证明:
四边形H1H2H3H4≌四边形ABCD.
证明 只需证H1H2(⊥)AB.
若设四边形ABCD的外接圆圆心为0,则由赛尔维斯特定理得
→OH1=→OB+→OC+→OD,→OH2=→OA+→OC+→OD.
于是,→H1H2=→BA.
由此易知结论成立.
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