作者Honor1984 (奈何上天造化弄人？)
看板Math
标题Re: [中学] 向量1题
时间Sat Jan 16 03:42:34 2021
※ 引述《hero010188 (我是海贼王)》之铭言：
: https://i.imgur.com/SkSNFph.jpg
: 答案是外心 想问推导过程 感谢
OA^2 + BC^2 = OB^2 + AC^2 = OC^2 + AB^2
=> OC * OB = OC * OA = OB * OA
=> OC * AB = OB * AC = OA * BC = 0
=> O是垂心 = H
OP = (1/2)[OA + OB + OC]
=> HP = (3/2)HG
因为2O'G = GH，O'为外心
=> HP = -3O'G = -O'H
=> P = O'外心
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