PUMaC 2017 · 几何（B 组） · 第 1 题
PUMaC 2017 — Geometry (Division B) — Problem 1
题目详情
- Equilateral triangle ABC has area 1. A , B and C are the midpoints of BC , CA and AB , ′′ ′′ ′′ ′ ′ ′ ′ ′ ′ respectively. A , B and C are the midpoints of B C , C A and A B , respectively. The m ′′ ′′ area of trapezoid BB C C can be written as for relatively prime positive integers m and n n . Find m + n .
解析
- Note that CC A A and AA B B are congruent to BB C C , and their area combined with the innermost triangle is equal to the total area. Call their area K . Then, since the inner 1 1 5 triangle has sides those of the larger triangle, 3 K + = 1, so K = , getting final answer 4 16 16 21 . ( ) 2 d