HMMT 二月 2012 · 几何 · 第 5 题
HMMT February 2012 — Geometry — Problem 5
题目详情
- A mouse lives in a circular cage with completely reflective walls. At the edge of this cage, a small ◦ ◦ flashlight with vertex on the circle whose beam forms an angle of 15 is centered at an angle of 37 . 5 away from the center. The mouse will die in the dark. What fraction of the total area of the cage can keep the mouse alive? ◦
解析
- A mouse lives in a circular cage with completely reflective walls. At the edge of this cage, a small ◦ ◦ flashlight with vertex on the circle whose beam forms an angle of 15 is centered at an angle of 37 . 5 away from the center. The mouse will die in the dark. What fraction of the total area of the cage can keep the mouse alive? ◦