View source for File:AIME 2005I Solution 7 1.png

defaultpen(fontsize(8));
pair A=(0,0), B=(9+sqrt(141),0), C=(5+sqrt(141),4*sqrt(3)), D=(5,5*sqrt(3)), E=(5,0), F=(5+sqrt(141),0), G=(5,4*sqrt(3));
draw(A--B--C--D--A);draw(D--E);draw(C--F);draw(G--C);
dot(A^^B^^C^^D^^E^^F^^G);
label("A",A,(-1,-1));label("B",B,(1,-1));label("C",C,(1,1));label("D",D,(-1,1));
label("E",E,(0,-1));label("F",F,(0,-1));label("G",G,(1,-1));
label("$10$",D/2,(-1,1));label("$12$",D/2+C/2,(1/2,1));label("$8$",C/2+B/2,(1,0));
label("$4$",F/2+B/2,(0,-1));label("$5$",E/2,(0,-1));