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HMMT 十一月 2013 · 冲刺赛 · 第 31 题

HMMT November 2013 — Guts Round — Problem 31

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 17 ] Chords AB and CD of circle ω intersect at E such that AE = 8, BE = 2, CD = 10, and
    °
    ∠ AEC = 90 . Let R be a rectangle inside ω with sides parallel to AB and CD , such that no point inthe interior of R lies on AB , CD , or the boundary of ω . What is the maximum possible area of R ?
解析

英文解析

  1. [ 17 ] Chords AB and CD of circle ω intersect at E such that AE = 8, BE = 2, CD = 10, and
    °
    ∠ AEC = 90 . Let R be a rectangle inside ω with sides parallel to AB and CD , such that no point inthe interior of R lies on AB , CD , or the boundary of ω . What is the maximum possible area of R ?
    √
    Answer: 26 + 6 17 By power of a point, ( CE )( ED ) = ( AE )( EB ) = 16, and CE + ED = CD =