PUMaC 2009 · 几何（B 组） · 第 6 题
PUMaC 2009 — Geometry (Division B) — Problem 6
题目详情
- In the following diagram (not to scale), A , B , C , D are four consecutive vertices of an 18-sided regular polygon with center O . Let P be the midpoint of AC and Q be the midpoint of DO . Find ∠ OP Q in degrees.
解析
- In the following diagram (not to scale), A , B , C , D are four consecutive vertices of an 18-sided regular polygon with center O . Let P be the midpoint of AC and Q be the midpoint of DO . Find ∠ OP Q in degrees. Solution. 30. Let R be the midpoint of AO . Connect RP , RQ . Then RP = RO = OQ = RQ . Hence triangle P QR is isosceles, then some simple calculation yields ∠ OP Q = ◦ ◦ ◦ ∠ RP Q − ∠ RP O = 50 − 20 = 30 . 2