HMMT 二月 2001 · GEN2 赛 · 第 5 题
HMMT February 2001 — GEN2 Round — Problem 5
题目详情
- What is the area of a square inscribed in a semicircle of radius 1, with one of its sides flush with the diameter of the semicircle?
解析
- What is the area of a square inscribed in a semicircle of radius 1, with one of its sides flush with the diameter of the semicircle? Solution: Call the center of the semicircle O , a point of contact of the square and the circular part of the semicircle A , the closer vertex of the square on the diameter B , and the x side length of the square x . We know OA = 1, AB = x , OB = , and ∠ ABO is right. By 2 2 4 the Pythagorean theorem, x = . 5