返回题库

HMMT 二月 2007 · TEAM2 赛 · 第 9 题

HMMT February 2007 — TEAM2 Round — Problem 9

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 20 ] Cyclic quadrilateral ABCD has side lengths AB = 1 , BC = 2 , CD = 3 , and AD = 4. Determine
    AC/BD.
解析

英文解析

  1. [ 20 ] Cyclic quadrilateral ABCD has side lengths AB = 1 , BC = 2 , CD = 3 , and AD = 4. Determine
    AC/BD.
    Answer: 5 / 7 . Let the diagonals intersect at P. Note that triangles ABP and DCP are similar,
    so that 3 AP = DP and 3 BP = CP. Additionally, triangles BCP and ADP are similar, so that
    2 BP = AP. It follows that
    AC AP + P C 2 BP + 3 BP 5 = = = .
    BD BP + P D BP + 6 BP 7 2