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HMMT 二月 2001 · 冲刺赛 · 第 26 题

HMMT February 2001 — Guts Round — Problem 26

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [6] A circle with center at O has radius 1. Points P and Q outside the circle areplaced such that P Q passes through O . Tangent lines to the circle through P hit the circleat 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 angle q QQ = 30 , find the minimum possible length of arc P Q .
    1 2 1 2 2 2
解析

英文解析

  1. [6] A circle with center at O has radius 1. Points P and Q outside the circle areplaced such that P Q passes through O . Tangent lines to the circle through P hit the circleat 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 angle q QQ = 30 , find the minimum possible length of arc P Q .
    1 2 1 2 2 2
    °π
    Solution: (45 − 30) = .
    12