Math Prize 2011 Problem 3
Source:
September 19, 2011
geometryvideos
Problem Statement
The figure below shows a triangle 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("", A, S);
label("", B, S);
label("", 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 , , and , what is the area of the shaded region?