HMMT 二月 2003 · 冲刺赛 · 第 24 题
HMMT February 2003 — Guts Round — Problem 24
题目详情
- [9] Compute the radius of the inscribed circle of a triangle with sides 15, 16, and 17. 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HARVARD-MIT MATHEMATICS TOURNAMENT, MARCH 15, 2003 — GUTS ROUND
解析
- 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 result that the area of a triangle equals the inradius times half the perimeter, we see that the √ radius is 21. 6