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HMMT 十一月 2009 · 团队赛 · 第 6 题

HMMT November 2009 — Team Round — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 4 ] Find the distance from the ball’s point of first contact with a wall to the nearest vertex.
解析

英文解析

  1. [ 4 ] Find the distance from the ball’s point of first contact with a wall to the nearest vertex.
    Answer: 2
    √MYB
    √519
    5 32
    A C52
    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 theoremagain, we see that M Y = , so that BY = 2.12 2