PUMaC 2009 · 几何（B 组） · 第 2 题
PUMaC 2009 — Geometry (Division B) — Problem 2
题目详情
- A triangle has sides of lengths 5, 6, 7. What is 60 times the square of the radius of the inscribed circle?
解析
- A triangle has sides of lengths 5, 6, 7. What is 60 times the square of the radius of the inscribed circle? Solution. 160. Use Heron’s Formula, and then the area of the triangle is √ √ 9 × (9 − 5) × (9 − 6) × (9 − 7) = 6 6 Hence radius of incircle is √ √ 2 × 6 6 2 6 = 5 + 6 + 7 3 .