Problems(1)
Diameter ACE is divided at C in the ratio 2:3. The two semicircles, ABC and CDE, divide the circular region into an upper (shaded) region and a lower region. The ratio of the area of the upper region to that of the lower region is[asy]pair A,B,C,D,EE;
A = (0,0); B = (2,2); C = (4,0); D = (7,-3); EE = (10,0);
fill(arc((2,0),A,C,CW)--arc((7,0),C,EE,CCW)--arc((5,0),EE,A,CCW)--cycle,gray);
draw(arc((2,0),A,C,CW)--arc((7,0),C,EE,CCW));
draw(circle((5,0),5));dot(A); dot(B); dot(C); dot(D); dot(EE);
label("A",A,W);
label("B",B,N);
label("C",C,E);
label("D",D,N);
label("E",EE,W);
[/asy]<spanclass=′latex−bold′>(A)</span> 2:3<spanclass=′latex−bold′>(B)</span> 1:1<spanclass=′latex−bold′>(C)</span> 3:2<spanclass=′latex−bold′>(D)</span> 9:4<spanclass=′latex−bold′>(E)</span> 5:2 ratiogeometryAMC