HMMT 二月 2016 · 几何 · 第 3 题
HMMT February 2016 — Geometry — Problem 3
题目详情
英文原题
- In the below picture, T is an equilateral triangle with a side length of 5 and ω is a circle with a radiusof 2. The triangle and the circle have the same center. Let X be the area of the shaded region, andlet Y be the area of the starred region. What is X − Y ?
ωT
解析
英文解析
- In the below picture, T is an equilateral triangle with a side length of 5 and ω is a circle with a radiusof 2. The triangle and the circle have the same center. Let X be the area of the shaded region, andlet Y be the area of the starred region. What is X − Y ?
Proposed by:ωT
√
25 3 4 π
Answer: −
12 3
Let K ( P ) denote the area of P . Note that K ( T ) − K ( ω ) = 3( X − Y ), which gives our answer.