Find the radius of circle O
Source: 1976 AHSME Problem 18
May 18, 2014
geometrypower of a pointAMC
Problem Statement
[asy]
//size(100);//local
size(200);
real r1=2;
pair
O=(0,0),
D=(.5,.5*sqrt(3)),
C=(D.x+.5*3,D.y),
B,
B_prime=endpoint(arc(D, 3, 0,-2));
B=B_prime;
path
c1=circle(O, r1);
pair C=midpoint(D--B_prime);
path arc2=arc(B_prime, 6/2, 158.25,250);
draw(c1);
draw(O--D);
draw(D--C);
draw(C--B_prime);
pair A=beginpoint(arc2);
draw(B_prime--A);
//dot(O^^D^^C^^A);
//dot(B_prime);
label("\scriptsize{}",O,.6dir(D--O));
label("\scriptsize{}",C,.5dir(-55));
label("\scriptsize{}", D,.2NW);
//label("\scriptsize{}",B,S);
label("\scriptsize{}", B_prime, .5*dir(D--B_prime));
label("\scriptsize{}",A,.5dir(NE));
label("\tiny{2}", O--D, .45*LeftSide);
label("\tiny{3}", D--C, .45*LeftSide);
label("\tiny{6}", B_prime--A, .45*RightSide);
label("\tiny{3}", waypoint(C--B_prime,.1), .45*N);
//Credit to Klaus-Anton for the diagram[/asy]In the adjoining figure, is tangent at to the circle with center ; point is interior to the circle; and intersects the circle at . If , , and , then the radius of the circle is