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