Math Prize 2010 Problem 11
Source:
November 14, 2010
geometryrhombus
Problem Statement
In the figure below, each side of the rhombus has length 5 centimeters.
[asy]
import graph;
unitsize(2.0cm);
real w = sqrt(3);
draw((w, 0) -- (0, 1) -- (-w, 0) -- (0, -1) -- cycle);
filldraw(Circle((-0.5, 0), 0.8 / sqrt(pi)), gray);
label("", (w - 0.1, 0), W);
[/asy]
The circle lies entirely within the rhombus. The area of the circle is square centimeters, where is a positive integer. Compute the number of possible values of .