20
Part of 2004 AMC 10
Problems(2)
Problem: 2004 AMC 10 #20
Source:
2/1/2007
Points and are located on square so that is equilateral. What is the ratio of the area of to that of ?[asy]
pair A=origin, B=(1,0), C=(1,1), D=(0,1), X=B+2*dir(165), E=intersectionpoint(B--X, A--D), Y=B+2*dir(105), F=intersectionpoint(B--Y, D--C);
draw(B--C--D--A--B--F--E--B);
pair point=(0.5,0.5);
label("", A, dir(point--A));
label("", B, dir(point--B));
label("", C, dir(point--C));
label("", D, dir(point--D));
label("", E, dir(point--E));
label("", F, dir(point--F));[/asy]
ratiogeometry
Intersecting Lines in a Triangle
Source:
1/15/2009
In points and lie on and , respectively. If and intersect at so that AT/DT \equal{} 3 and BT/ET \equal{} 4, what is ?
[asy]unitsize(2cm);
defaultpen(linewidth(.8pt));pair A = (0,0);
pair C = (2,0);
pair B = dir(57.5)*2;
pair E = waypoint(C--A,0.25);
pair D = waypoint(C--B,0.25);
pair T = intersectionpoint(D--A,E--B);label("",B,NW);label("",A,SW);label("",C,SE);label("",D,NE);label("",E,S);label("",T,2*W+N);draw(A--B--C--cycle);
draw(A--D);
draw(B--E);[/asy]
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