HMMT 十一月 2011 · 冲刺赛 · 第 2 题
HMMT November 2011 — Guts Round — Problem 2
题目详情
英文原题
[5] Let ABCD be a rectangle with AB= 6 and BC= 4. Let Ebe the point on BCwithBE= 3, and let Fbe the point on segment AEsuch that Flies halfway between the segments ABandCD. If Gis the point of intersection of DFandBC, find BG.
解析
英文解析
- [ 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 besymmetric about the line through F parallel to AB . Hence, G must be the reflection of E across themidpoint of BC . Therefore, BG = EC = 1.
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