HMMT 二月 1998 · 几何 · 第 5 题
HMMT February 1998 — Geometry — Problem 5
题目详情
英文原题
Question Five . [5 points]
Square SEAN has side length 2 and a NSquarter-circle of radius 1 around E is cutout.
Find the radius of the largest circle thatcan be inscribed in the remaining figure.
A E
解析
英文解析
- If the new circle has radius r , then the distance from its center to E can be computed either
√
√
√
2 2 − 1
√
as 1 + r or (2 − r ) 2. Setting these equal yields r = = 5 − 3 2 .
2+1
( )
1 π2
√