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HMMT 二月 2003 · 冲刺赛 · 第 24 题

HMMT February 2003 — Guts Round — Problem 24

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. [9] Compute the radius of the inscribed circle of a triangle with sides 15, 16, and 17.
    HARVARD-MIT MATHEMATICS TOURNAMENT, MARCH 15, 2003 — GUTS ROUND

英文原题

[9] Compute the radius of the inscribed circle of a triangle with sides 15, 16, and 17.
3
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HARVARD-MIT MATHEMATICS TOURNAMENT, MARCH 15, 2003 — GUTS ROUND

解析

英文解析

  1. Compute the radius of the inscribed circle of a triangle with sides 15, 16, and 17.
    √
    Solution: 21
    √ √
    Hero’s formula gives that the area is 24 · 9 · 8 · 7 = 24 21. Then, using the resultthat the area of a triangle equals the inradius times half the perimeter, we see that the
    √
    radius is 21. 6