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HMMT 二月 2003 · 冲刺赛 · 第 10 题

HMMT February 2003 — Guts Round — Problem 10

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [7] Suppose that A, B, C, D are four points in the plane, and let Q, R, S, T, U, V be therespective midpoints of AB, AC, AD, BC, BD, CD . If QR = 2001 , SU = 2002 , T V =
    2003, find the distance between the midpoints of QU and RV .
    2 2 2 2 2
解析

英文解析

  1. Suppose that A, B, C, D are four points in the plane, and let Q, R, S, T, U, V be therespective midpoints of AB, AC, AD, BC, BD, CD . If QR = 2001 , SU = 2002 , T V =
    2003, find the distance between the midpoints of QU and RV .
    Solution: 2001
    This problem has far more information than necessary: QR and U V are both parallelto BC , and QU and RV are both parallel to AD . Hence, QU V R is a parallelogram,
    and the desired distance is simply the same as the side length QR , namely 2001. (Seefigure, next page.)
    2 2 2 2 2