HMMT 二月 2018 · 几何 · 第 1 题
HMMT February 2018 — Geometry — Problem 1
题目详情
- Triangle GRT has GR = 5, RT = 12, and GT = 13. The perpendicular bisector of GT intersects the extension of GR at O . Find T O .
解析
- Triangle GRT has GR = 5, RT = 12, and GT = 13. The perpendicular bisector of GT intersects the extension of GR at O . Find T O . Proposed by: Henrik Boecken 169 Answer: 10 First, note that T O = GO as O lies on the perpendicular bisector of GT . Then if M is the midpoint GT 13 13 169 of GT , we have that 4 GRT ∼ 4 GM O , so we can compute T O = GO = GM · = · = . GR 2 5 10