HMMT 十一月 2011 · 冲刺赛 · 第 2 题

HMMT November 2011 — Guts Round — Problem 2

[ 5 ] Let ABCD be a rectangle with AB = 6 and BC = 4. Let E be the point on BC with BE = 3, and let F be the point on segment AE such that F lies halfway between the segments AB and CD . If G is the point of intersection of DF and BC , find BG . x 3 x +2

解析

[ 5 ] Let ABCD be a rectangle with AB = 6 and BC = 4. Let E be the point on BC with BE = 3, and let F be the point on segment AE such that F lies halfway between the segments AB and CD . If G is the point of intersection of DF and BC , find BG . Answer: 1 Note that since F is a point halfway between AB and AC , the diagram must be symmetric about the line through F parallel to AB . Hence, G must be the reflection of E across the midpoint of BC . Therefore, BG = EC = 1. x 3 x +2