Three Externally Tangent Circles
Source:
January 15, 2009
ratio
Problem Statement
Three circles of radius are externally tangent to each other and internally tangent to a larger circle. What is the radius of the large circle?
[asy]unitsize(0.8cm);
defaultpen(linewidth(.8pt)+fontsize(8pt));real r = 1 + (2/3)*(sqrt(3));
pair A = dir(47.5)*(r - 1);
pair B = dir(167.5)*(r - 1);
pair C = dir(-72.5)*(r - 1);draw(Circle(A,1));
draw(Circle(B,1));
draw(Circle(C,1));
draw(Circle(origin,r));[/asy]
(A)\ \frac{2 \plus{} \sqrt{6}}{3}\qquad
(B)\ 2\qquad
(C)\ \frac{2 \plus{} 3\sqrt{2}}{3}\qquad
(D)\ \frac{3 \plus{} 2\sqrt{3}}{3}\qquad
(E)\ \frac{3 \plus{} \sqrt{3}}{2}