返回题库

HMMT 二月 2008 · TEAM2 赛 · 第 11 题

HMMT February 2008 — TEAM2 Round — Problem 11

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 15 ] Show that lines AD, BE, CF pass through a common point.
解析
  1. [ 15 ] Show that lines AD, BE, CF pass through a common point. Solution: Using Ceva’s theorem on triangle ABC , we see that it suffices to show that BD CE AF · · = 1 . DC EA F B Since AF = AE , BD = BF , and CD = CE (due to equal tangents), we see that the LHS is indeed 1. Remark: The point of concurrency is known as the Gergonne point .