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