PUMaC 2020 · 几何（A 组） · 第 3 题
PUMaC 2020 — Geometry (Division A) — Problem 3
题目详情
- Let ABCD be a cyclic quadrilateral with circumcenter O and radius 10 . Let sides AB, BC, CD, and DA have midpoints M, N, P, and Q, respectively. If M P = N Q and OM + OP = 16 , then what is the area of triangle 4 OAB ?
解析
- Let ABCD be a cyclic quadrilateral with circumcenter O and radius 10 . Let sides AB, BC, CD, and DA have midpoints M, N, P, and Q, respectively. If M P = N Q and OM + OP = 16 , then what is the area of triangle 4 OAB ? Proposed by: Ollie Thakar Answer: 78 Note: The configuration provided in this problem turned out to be impossible, since we arrive at 2 2 the condition OM + OP = 100 , which cannot hold with the given condition that OM + OP =