Math Prize 2010 Problem 14
Source:
November 14, 2010
geometry
Problem Statement
In the figure below, the three small circles are congruent and tangent to each other. The large circle is tangent to the three small circles.
[asy]
import graph;
unitsize(20);
real r = sqrt(3) / 2;
filldraw(Circle((0, 0), 1 + r), gray);
filldraw(Circle(dir(90), r), white);
filldraw(Circle(dir(210), r), white);
filldraw(Circle(dir(330), r), white);
[/asy]
The area of the large circle is 1. What is the area of the shaded region?