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HMMT 十一月 2010 · 冲刺赛 · 第 16 题

HMMT November 2010 — Guts Round — Problem 16

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 9 ] Triangle ABC is given in the plane. Let AD be the angle bisector of ∠ BAC ; let BE be the altitudefrom B to AD , and let F be the midpoint of AB . Given that AB = 28 , BC = 33 , CA = 37, what isthe length of EF ?
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解析

英文解析

  1. [ 9 ] Triangle ABC is given in the plane. Let AD be the angle bisector of ∠ BAC ; let BE be the altitudefrom B to AD , and let F be the midpoint of AB . Given that AB = 28 , BC = 33 , CA = 37, what isthe length of EF ?
    Answer: 14 4 ABE is a right triangle, and F is the midpoint of the hypotenuse (and therefore thecircumcenter), so EF = BF = AF = 14.