HMMT 二月 2009 · 几何 · 第 3 题
HMMT February 2009 — Geometry — Problem 3
题目详情
- [ 4 ] Let T be a right triangle with sides having lengths 3, 4, and 5. A point P is called awesome if P is 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
- [ 4 ] Let T be a right triangle with sides having lengths 3, 4, and 5. A point P is called awesome if P is the center of a parallelogram whose vertices all lie on the boundary of T . What is the area of the set of awesome points? Answer: 3 / 2 Solution: The set of awesome points is the medial triangle, which has area 6 / 4 = 3 / 2.