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HMMT 十一月 2017 · 冲刺赛 · 第 26 题

HMMT November 2017 — Guts Round — Problem 26

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 15 ] Points A, B, C, D lie on a circle in that order such that = . If AC = 3 and BD = BC = 4, BC CD find AD . 1
解析
  1. [ 15 ] Points A, B, C, D lie on a circle in that order such that = . If AC = 3 and BD = BC = 4, BC CD find AD . Proposed by: Yuan Yao 3 Answer: 2 By Ptolemy’s theorem, we have AB · CD + BC · DA = AC · BD = 3 · 4 = 12. Since the condition 6 3 implies AB · CD = BC · DA , we have DA = = . BC 2 1