HMMT 十一月 2009 · 团队赛 · 第 1 题

HMMT November 2009 — Team Round — Problem 1

解析

[ 3 ] Find the radius of ω . 1 10 Answer: Using the Pythagorean theorem, we see that the legs of T each have length 13. Let r 3 be the radius of ω . We can divide T into three triangles, each with two vertices at vertices of T and 1 one vertex at the center of ω . These triangles all have height r and have bases 13, 13, and 10. Thus 1 13 r 13 r 10 r their total area is + + = 18 r . However, T has height 12 and base 10, so its area is 60. Thus 2 2 2 10 18 r = 60, so r = . 3