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HMMT 十一月 2009 · 团队赛 · 第 6 题

HMMT November 2009 — Team Round — Problem 6

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 4 ] Find the distance from the ball’s point of first contact with a wall to the nearest vertex.
解析
  1. [ 4 ] Find the distance from the ball’s point of first contact with a wall to the nearest vertex. Answer: 2 B Y M √ 19 5 √ 2 5 3 2 5 A C Consider the diagram above, where M is the midpoint of BC . Then AM is perpendicular to BC since √ 5 3 ABC is equilateral, so by the Pythagorean theorem AM = . Then, using the Pythagorean theorem 2 1 again, we see that M Y = , so that BY = 2. 2