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HMMT 十一月 2022 · 冲刺赛 · 第 11 题

HMMT November 2022 — Guts Round — Problem 11

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [8] Isosceles trapezoid ABCD with bases AB and CD has a point P on AB with AP = 11, BP = 27, ◦ CD = 34, and ∠ CP D = 90 . Compute the height of isosceles trapezoid ABCD.
解析
  1. [8] Isosceles trapezoid ABCD with bases AB and CD has a point P on AB with AP = 11, BP = 27, ◦ CD = 34, and ∠ CP D = 90 . Compute the height of isosceles trapezoid ABCD. Proposed by: Albert Wang Answer: 15 ′ ′ ′ ′ ′ Solution: Drop projections of A , P , B onto CD to get A , P , B . Since A B = 38 and CD = 34, we √ ′ ′ ′ ′ ′ ′ ′ get that DA = CB = 2. Thus, P D = 9 and P C = 25. Hence, the answer is P P = P D · P C =