17
Part of 2006 AMC 10
Problems(2)
2006 AMC 10 #17
Source:
8/20/2011
In rectangle , points and trisect , and points and trisect . In addition, AH \equal{} AC \equal{} 2. What is the area of quadrilateral shown in the figure?[asy]defaultpen(linewidth(0.7));pointpen=black; pathpen=black;
size(7cm);
pair A,B,C,D,E,F,G,H,W,X,Y,Z;
A=(0,2); B=(1,2); C=(2,2); D=(3,2);
H=(0,0); G=(1,0); F=(2,0); E=(3,0);
D('A',A, N); D('B',B,N); D('C',C,N); D('D',D,N); D('E',E,NE); D('F',F,NE); D('G',G,NW); D('H',H,NW);
D(A--F); D(B--E); D(D--G); D(C--H);
Z=IP(A--F, C--H); Y=IP(A--F, D--G); X=IP(B--E,D--G); W=IP(B--E,C--H);
D('W',W,N); D('X',X,plain.E); D('Y',Y,S); D('Z',Z,plain.W);
D(A--D--E--H--cycle);[/asy]
geometryrectanglecongruent triangles
Choosing balls
Source: AMC 10 2006B, Problem 17
2/17/2006
Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that after this process, the contents of the two bags are the same?
probabilitysymmetryAMC