HMMT 十一月 2009 · 团队赛 · 第 1 题

英文解析

1. [ 3 ] Find the radius of ω .
   Answer: Using the Pythagorean theorem, we see that the legs of T each have length 13. Let r 101
   be the radius of ω . We can divide T into three triangles, each with two vertices at vertices of T and 3
   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 1
   their total area is + + = 18 r . However, T has height 12 and base 10, so its area is 60. Thus
   2 2 2
   18 r = 60, so r = .10 3