Circles C_{1} and C_{2} each have radius 1 , and the distance between their centers is \dfrac{1}{2}. Circle C_{3} is the largest circle internally tangent to both C_{1} and C_{2}. Circle C_{4} is internally tangent to both C_{1} and C_{2} and externally tangent to C_{3}. What is the radius of C_{4}?

**Answer Choices**

A. \dfrac{1}{14}

B. \dfrac{1}{12}

C. \dfrac{1}{10}

D. \dfrac{3}{28}

E. \dfrac{1}{9}