返回题库

HMMT 二月 2011 · TEAM2 赛 · 第 11 题

HMMT February 2011 — TEAM2 Round — Problem 11

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 10 ] Let H be the intersection of the three altitudes of triangle ABC . (This point is usually called the orthocenter). Prove that ∠ DAH = ∠ M AO .
解析
  1. [ 10 ] Let H be the intersection of the three altitudes of triangle ABC . (This point is usually called the orthocenter). Prove that ∠ DAH = ∠ M AO . Solution: Note that since both AH and OX are perpendicular to BC , it follows that AH ‖ OX , so ∠ DAH = ∠ DXO = ∠ AXO = ∠ M AO , as desired.