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PUMaC 2013 · 几何（B 组） · 第 1 题

PUMaC 2013 — Geometry (Division B) — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 3 ] We construct three circles: O with diameter AB and area 12 + 2 x , P with diameter AC and area 24 + x , and Q with diameter BC and area 108 − x . Given that C is on circle O , compute x . ◦
解析
  1. [ 3 ] We construct three circles: O with diameter AB and area 12 + 2 x , P with diameter AC and area 24 + x , and Q with diameter BC and area 108 x . Given that C is on circle O , compute x . Solution Pythagorean theorem gives the answer immediately. We should have 12 + 2 x = 24 + x + 108 x , or x = 60 .