Points of Tangency
Source:
February 8, 2009
Problem Statement
In the diagram, if points , and are points of tangency, then equals:
[asy]unitsize(5cm);
defaultpen(linewidth(.8pt)+fontsize(8pt));
dotfactor=3;pair A=(-3*sqrt(3)/32,9/32), B=(3*sqrt(3)/32, 9/32), C=(0,9/16);
pair O=(0,3/8);draw((-2/3,9/16)--(2/3,9/16));
draw((-2/3,1/2)--(-sqrt(3)/6,1/2)--(0,0)--(sqrt(3)/6,1/2)--(2/3,1/2));
draw(Circle(O,3/16));
draw((-2/3,0)--(2/3,0));label("",A,SW);
label("",B,SE);
label("",C,N);
label("",O);
draw(O+.07*dir(60)--O+3/16*dir(60),EndArrow(3));
draw(O+.07*dir(240)--O+3/16*dir(240),EndArrow(3));
label("",(.5,.25));
draw((.5,.33)--(.5,.5),EndArrow(3));
draw((.5,.17)--(.5,0),EndArrow(3));
label("",midpoint((.5,.5)--(.5,9/16)));
draw((.5,5/8)--(.5,9/16),EndArrow(3));
label("",(0.01,0.12));
dot(A);
dot(B);
dot(C);[/asy]