Question 51
Three equal circles are inscribed into the equilateral triangle with the sides of length $1$ (see figure). What is the length of the radii of the circles?
(A) $\frac{1}{3}$
(B) $\frac{1}{4}$
(C) $\frac{\sqrt{3}}{4}$
(D) $\frac{\sqrt{3}+1}{4}$
(E) $\frac{\sqrt{3}-1}{4}$
(A) $\frac{1}{3}$
(B) $\frac{1}{4}$
(C) $\frac{\sqrt{3}}{4}$
(D) $\frac{\sqrt{3}+1}{4}$
(E) $\frac{\sqrt{3}-1}{4}$