Purple Comet 2009 HS Problem 7
Source:
April 21, 2012
geometryAsymptote
Problem Statement
The figure is bounded by a semicircle and a quarter circle . Given that the distance from to is , find the area of the figure.[asy]
size(200);
defaultpen(linewidth(0.8));
pair A=(-9,0),B=(0,9*sqrt(2)-9),C=(9,0),D=(0,9);
dot(A^^B^^C^^D);
draw(arc(origin,9,0,180)^^arc((0,-9),9*sqrt(2),45,135));
label("",A,S);
label("",B,N);
label("",C,S);
label("",D,N);
[/asy]