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HMMT 二月 2011 · TEAM2 赛 · 第 13 题

HMMT February 2011 — TEAM2 Round — Problem 13

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 10 ] Prove that line AD is also the symmedian from D in triangle DBC .
    Last Writes [65]
    The problems in this section require complete proofs .
解析

英文解析

  1. [ 10 ] Prove that line AD is also the symmedian from D in triangle DBC .
    Solution: In the previous problems, we showed that the symmedian from A in triangle ABC is the line AX , where X is the intersection of the tangents to the circumcircle at B and C . Since the choiceof triangle was arbitrary, we may conclude that DX is the symmedian from D in triangle DBC . Since
    A , D , and X , are collinear, this completes the proof.
    Team Round B
    Last Writes [65]
    The problems in this section require complete proofs .