HMMT 二月 2001 · GEN2 赛 · 第 5 题

英文解析

5. What is the area of a square inscribed in a semicircle of radius 1, with one of its sidesflush with the diameter of the semicircle?
   Solution: Call the center of the semicircle O , a point of contact of the square and thecircular part of the semicircle A , the closer vertex of the square on the diameter B , and theside length of the square x . We know OA = 1, AB = x , OB = , and ∠ ABO is right. Byx
   2 42
   the Pythagorean theorem, x = . 5