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HMMT 二月 2002 · GEN2 赛 · 第 9 题

HMMT February 2002 — GEN2 Round — Problem 9

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. A and B are two points on a circle with center O , and C lies outside the circle, on ray AB . Given that AB = 24 , BC = 28 , OA = 15, find OC .
解析
  1. A and B are two points on a circle with center O , and C lies outside the circle, on ray AB . Given that AB = 24 , BC = 28 , OA = 15, find OC . Solution: 41 . Let M be the midpoint of AB ; then 4 OM B is a right triangle with OB = 15 , M B = 12, so OM = 9. Now 4 OM C is a right triangle with OM = 9 , M C = 40, so OC = 41.