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PUMaC 2013 · 几何（A 组） · 第 7 题

PUMaC 2013 — Geometry (Division A) — Problem 7

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 7 ] Given triangle ABC and a point P inside it, ∠ BAP = 18 , ∠ CAP = 30 , ∠ ACP = 48 , ◦ and AP = BC . If ∠ BCP = x , find x .
解析
  1. [ 7 ] Given triangle ABC and a point P inside it, \ BAP = 18 , \ CAP = 30 , \ ACP = 48 , and AP = BC . If \ BCP = x , find x . Solution Observe \ BAC = \ ACP = 48 . Draw a line through P parallel to AC and let it cut AB at Q . Then ACP Q is an isosceles trapezoid. Thus we have BC = AP = CQ and hence \ ABC = \ BQC = 48 + 30 = 78 , giving \ BCP = 6 .