SMO 2017 Open Round 1 Question 25

In a triangle $ABC$, $AB=AC$, $BC=22\sqrt3$, $\cos A=-\frac{17}{225}$, $D$ is a point on $AC$ such that $AD\lt DC$ and $P$ is the point on the segment $BD$ such that $\angle APC=90^\circ$. Given $\angle ABD=\angle BCP$, find $BD$.