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HMMT 十一月 2015 · THM 赛 · 第 1 题

HMMT November 2015 — THM Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. Consider a 1 × 1 grid of squares. Let A, B, C, D be the vertices of this square, and let E be the midpointof segment CD . Furthermore, let F be the point on segment BC satisfying BF = 2 CF , and let P bethe intersection of lines AF and BE . Find .AP
    P F
解析

英文解析

  1. Consider a 1 × 1 grid of squares. Let A, B, C, D be the vertices of this square, and let E be the midpointof segment CD . Furthermore, let F be the point on segment BC satisfying BF = 2 CF , and let P bethe intersection of lines AF and BE . Find .AP
    P F
    Proposed by: Sam Korsky
    Answer: 3
    Let line BE hit line DA at Q . It’s clear that triangles AQP and F BP are similar so
    AP AQ 2 AD = = = 3
    P F BF2
    3BC