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HMMT 十一月 2014 · 冲刺赛 · 第 7 题

HMMT November 2014 — Guts Round — Problem 7

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 7 ] Let ABCD be a quadrilateral inscribed in a circle with diameter AD . If AB = 5, AC = 6, and
    BD = 7, find CD .
    41
解析

英文解析

  1. [ 7 ] Let ABCD be a quadrilateral inscribed in a circle with diameter AD . If AB = 5, AC = 6, and
    BD = 7, find CD .
    √ √ √
    2 2 2 2 2
    2 2 2
    Answer: 38 We have AD = AB + BD = AC + CD , so CD = AB + BD − AC = 38.
    41