Question 57
Let $ABC$ be a triangle with a right angle at $C$ and sides $BC=3$ and $AB=12$. Let $M$ be the midpoint of $AB$, and $D$ the intersection of $AC$ with the circumcircle of $BCM$. Finally, let $P$ be the intersection point of $BC$ and $MD$. What is the length of segment $PA$?
(A) $\frac{28}{5} \sqrt{15}$
(B) $6 \sqrt{15}$
(C) $24$
(D) $12 \sqrt{15}$
(E) $48$
(A) $\frac{28}{5} \sqrt{15}$
(B) $6 \sqrt{15}$
(C) $24$
(D) $12 \sqrt{15}$
(E) $48$