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HMMT 二月 2009 · GEN2 赛 · 第 10 题

HMMT February 2009 — GEN2 Round — Problem 10

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] Let T be a right triangle with sides having lengths 3, 4, and 5. A point P is called “awesome” if Pis the center of a parallelogram whose vertices all lie on the boundary of T . What is the area of the set of awesome points?
解析

英文解析

  1. [ 6 ] Let T be a right triangle with sides having lengths 3, 4, and 5. A point P is called awesome if P isthe center of a parallelogram whose vertices all lie on the boundary of T . What is the area of the setof awesome points?
    Answer: 3 / 2
    Solution: The set of awesome points is the medial triangle, which has area 6 / 4 = 3 / 2. 3