Let \triangle A B C be a scalene triangle. Point P lies on \overline{B C} so that \overline{A P} bisects \angle B A C. The line through B perpendicular to \overline{A P} intersects the line through A parallel to \overline{B C} at point D. Suppose B P=2 and P C=3. What is A D ?

**Answer Choices**

A. 8

B. 9

C. 10

D. 11

E. 12