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3

Part of 2011 Math Prize For Girls Problems

Problems(1)

Math Prize 2011 Problem 3

Source:

9/19/2011
The figure below shows a triangle ABCABC with a semicircle on each of its three sides. [asy] unitsize(5); pair A = (0, 20 * 21) / 29.0; pair B = (-20^2, 0) / 29.0; pair C = (21^2, 0) / 29.0; draw(A -- B -- C -- cycle); label("AA", A, S); label("BB", B, S); label("CC", C, S); filldraw(arc((A + C)/2, C, A)--cycle, gray); filldraw(arc((B + C)/2, C, A)--cycle, white); filldraw(arc((A + B)/2, A, B)--cycle, gray); filldraw(arc((B + C)/2, A, B)--cycle, white); [/asy] If AB=20AB = 20, AC=21AC = 21, and BC=29BC = 29, what is the area of the shaded region?
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