Geometry: Power of a Point & Mass Points · Medium problem

In $\triangle ABC$ the side lengths are $AB=10$, $CA=17$, and $BC=21$. Point $D$ lies on segment $BC$ with $BD=6$ and $DC=15$, and point $E$ lies on segment $CA$ with $CE:EA=1:2$. The cevians $AD$ and $BE$ meet at $P$. Find the length $AP$.