HMMT 二月 2011 · TEAM2 赛 · 第 13 题

HMMT February 2011 — TEAM2 Round — Problem 13

[ 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

[ 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 choice of 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 .