2022 AMC 10A Problem 13

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

\textbf{(A) } 8 \qquad \textbf{(B) } 9 \qquad \textbf{(C) } 10 \qquad \textbf{(D) } 11 \qquad \textbf{(E) } 12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.