HMMT 二月 2001 · 冲刺赛 · 第 26 题
HMMT February 2001 — Guts Round — Problem 26
题目详情
- [6] A circle with center at O has radius 1. Points P and Q outside the circle are placed such that P Q passes through O . Tangent lines to the circle through P hit the circle at P and P , and tangent lines to the circle through Q hit the circle at Q and Q . If 1 2 1 2 ◦ ◦ ∠ P P P = 45 and angleQ QQ = 30 , find the minimum possible length of arc P Q . 1 2 1 2 2 2
解析
- [6] A circle with center at O has radius 1. Points P and Q outside the circle are placed such that P Q passes through O . Tangent lines to the circle through P hit the circle at P and P , and tangent lines to the circle through Q hit the circle at Q and Q . If 1 2 1 2 ◦ ◦ ∠ P P P = 45 and angleQ QQ = 30 , find the minimum possible length of arc P Q . 1 2 1 2 2 2 π ◦ Solution: (45 − 30) = . 12