A point $D$ is chosen in the interior of the side $BC$ of an acute triangle $ABC$, and another point $P$ in the interior of the segment $AD$, but not lying on the median through $C$. This median (through $C$) intersects the circumcircle of a triangle $CPD$ at $K(\ne C)$. Prove that the circumcircle of triangle $AKP$ always passes through a fixed point $M(\ne A)$ independent of the choices of the points $D$ and $P.$