HMMT 二月 2001 · GEN2 赛 · 第 9 题
HMMT February 2001 — GEN2 Round — Problem 9
题目详情
- Two circles are concentric. The area of the ring between them is A . In terms of A , find the length of the longest chord contained entirely within the ring.
解析
- Two circles are concentric. The area of the ring between them is A . In terms of A , find the length of the longest chord contained entirely within the ring. 2 2 Solution: Let the radii of the circles be r and R > r , so A = π ( R − r ). By the √ √ A 2 2 Pythagorean theorem, the length of the chord is 2 R − r = 2 . π