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PUMaC 2016 · 几何（B 组） · 第 6 题

PUMaC 2016 — Geometry (Division B) — Problem 6

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. Let D , E , and F respectively be the feet of the altitudes from A , B , and C of acute triangle 4 ABC such that AF = 28, F B = 35 and BD = 45. Let P be the point on segment BE such that AP = 42. Find the length of CP .
解析
  1. First of all, BF · BA = BD · BC ⇒ DC = 4. We observe that AE · AC = AF · AB = 28 · 63 = 2 ◦ 2 1764 = AP . Thus ∠ AP C = 90 , and similarly, CP = CE · CA = CD · CB = 196. Therefore CP = 14 . Problem written by Mel Shu.