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HMMT 二月 2014 · 几何 · 第 6 题

HMMT February 2014 — Geometry — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. In quadrilateral ABCD , we have AB = 5 , BC = 6 , CD = 5 , DA = 4, and \ ABC = 90 . Let AC and
    BD meet at E . Compute .BEED
解析

英文解析

  1. In quadrilateral ABCD , we have AB = 5 , BC = 6 , CD = 5 , DA = 4, and ∠ ABC = 90 . Let AC and
    BD meet at E . Compute .BE
    √ √ED
    Answer: 3 We find that AC = 61, and applying the law of cosines to triangle ACD tells us that
    √
    (5)(6)
    √BE
    ∠ ADC = 120. Then is the ratio of the areas of triangles ABC and ADC , which is = 3.
    ED3
    (4)(5) 2