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HMMT 二月 2017 · 冲刺赛 · 第 6 题

HMMT February 2017 — Guts Round — 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. [ 6 ] Let ABCD be a convex quadrilateral with AC = 7 and BD = 17. Let M, P, N, Q be the midpoints
    2 2
    of sides AB, BC, CD, DA respectively. Compute M N + P Q
解析

英文解析

  1. [ 6 ] Let ABCD be a convex quadrilateral with AC = 7 and BD = 17. Let M, P, N, Q be the midpoints
    2 2
    of sides AB, BC, CD, DA respectively. Compute M N + P Q
    Proposed by: Sam Korsky
    Answer: 169
    M P N Q is a parallelogram whose side lengths are 3 . 5 and 8 . 5 so the sum of squares of its diagonals is
    2 2
    7 +17 = 169 2