Question 19
In the triangle $ABC$, $AB=AC$, $\angle A=90^\circ$, $D$ is the midpoint of $BC$, $E$ is the midpoint of $AC$ and $F$ is a point on $AB$ such that $BE$ intersects $CF$ at $P$ and $B,D,P,F$ lie on a circle. Let $AD$ intersect $CP$ at $H$. Given $AP=\sqrt5+2$, find the length of $PH$.