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circumcircle of AKP passes through fixed point independent choiced D,P

Source: Indian Postal Coaching 2009 set 4 p5

May 26, 2020
geometryFixed pointfixedcircumcircle

Problem Statement

A point DD is chosen in the interior of the side BCBC of an acute triangle ABCABC, and another point PP in the interior of the segment ADAD, but not lying on the median through CC. This median (through CC) intersects the circumcircle of a triangle CPDCPD at K(≠C)K(\ne C). Prove that the circumcircle of triangle AKPAKP always passes through a fixed point M(≠A)M(\ne A) independent of the choices of the points DD and P.P.
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