In \triangle A B C shown in the figure, A B=7, B C=8, C A=9, and \overline{A H} is an altitude. Points D and E lie on sides \overline{A C} and \overline{A B}, respectively, so that \overline{B D} and \overline{C E} are angle bisectors, intersecting \overline{A H} at Q and P, respectively. What is P Q ?
Answer Choices
A. 1
B. \dfrac{5}{8} \sqrt{3}
C. \dfrac{4}{5} \sqrt{2}
D. \dfrac{8}{15} \sqrt{5}
E. \dfrac{6}{5}