SMO 2006 Open Round 1 Question 12

In triangle $ABC$, $AB=14$, $BC=16$, $AC=26$. Let $M$ be the midpoint of $BC$, and $D$ the point on $BC$ such that $AD$ bisects $\angle BAC$. Let $P$ be the foot of the perpendicular from $B$ onto $AD$. Determine $PM$.