In \triangle A B C, A B=6, A C=8, B C=10, and D is the midpoint of \overline{B C}. What is the sum of the radii of the circles inscribed in \triangle A D B and \triangle A D C ?

**Answer Choices**

A. \sqrt{5}

B. \dfrac{11}{4}

C. 2 \sqrt{2}

D. \dfrac{17}{6}

E. 3