HMMT 十一月 2015 · THM 赛 · 第 1 题
HMMT November 2015 — THM Round — Problem 1
题目详情
- Consider a 1 × 1 grid of squares. Let A, B, C, D be the vertices of this square, and let E be the midpoint of segment CD . Furthermore, let F be the point on segment BC satisfying BF = 2 CF , and let P be AP the intersection of lines AF and BE . Find . P F
解析
- Consider a 1 × 1 grid of squares. Let A, B, C, D be the vertices of this square, and let E be the midpoint of segment CD . Furthermore, let F be the point on segment BC satisfying BF = 2 CF , and let P be AP the intersection of lines AF and BE . Find . 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 2 P F BF BC 3