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HMMT 十一月 2014 · GEN 赛 · 第 2 题

HMMT November 2014 — GEN Round — Problem 2

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. Let ABC be a triangle with ∠ B = 90 . Given that there exists a point D on AC such that AD = DCand BD = BC , compute the value of the ratio .AB
    8 12BC
解析

英文解析

  1. Let ABC be a triangle with ∠ B = 90 . Given that there exists a point D on AC such that AD = DCand BD = BC , compute the value of the ratio .AB
    √BC
    Answer: 3 D is the circumcenter of ABC because it is the midpoint of the hypotenuse.
    Therefore, DB = DA = DC because they are all radii of the circumcircle, so DBC is an equilateral
    √
    ° ° ° °ABtriangle, and ∠ C = 60 . This means that ABC is a 30 − 60 − 90 triangle, with = 3 .
    8 12BC