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11

Part of 2010 Math Prize For Girls Problems

Problems(1)

Math Prize 2010 Problem 11

Source:

11/14/2010
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("60āˆ˜60^\circ", (w - 0.1, 0), W); [/asy] The circle lies entirely within the rhombus. The area of the circle is nn square centimeters, where nn is a positive integer. Compute the number of possible values of nn.
geometryrhombus