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HMMT 二月 2001 · 冲刺赛 · 第 44 题

HMMT February 2001 — Guts Round — Problem 44

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [7] Through a point in the interior of a triangle ABC , three lines are drawn, one parallel to each side. These lines divide the sides of the triangle into three regions each. Let a , b , and c be the lengths of the sides opposite ∠ A , ∠ B , and ∠ C , respectively, and let ′ ′ ′ a , b , and c be the lengths of the middle regions of the sides opposite ∠ A , ∠ B , and ∠ C , ′ ′ ′ respectively. Find the numerical value of a /a + b /b + c /c .
解析
  1. [7] Through a point in the interior of a triangle ABC , three lines are drawn, one parallel to each side. These lines divide the sides of the triangle into three regions each. Let a , b , and c be the lengths of the sides opposite ∠ A , ∠ B , and ∠ C , respectively, and let ′ ′ ′ a , b , and c be the lengths of the middle regions of the sides opposite ∠ A , ∠ B , and ∠ C , ′ ′ ′ respectively. Find the numerical value of a /a + b /b + c /c . Solution: 1 .