Question 49
Three circles of radius one are mutually tangent, and a fourth circle is tangent to all three and does not enclose them. What is the radius of the fourth circle?
(A) $\frac{\sqrt{3}+1}{24}$
(B) $\frac{1}{8}$
(C) $\frac{\sqrt{3}}{12}$
(D) $\frac{2 \sqrt{3}}{3}-1$
(E) $\frac{\sqrt{3}-1}{4}$
(A) $\frac{\sqrt{3}+1}{24}$
(B) $\frac{1}{8}$
(C) $\frac{\sqrt{3}}{12}$
(D) $\frac{2 \sqrt{3}}{3}-1$
(E) $\frac{\sqrt{3}-1}{4}$