Two Concyclic Quadruples

Geometry Level 3

Triangle ABCABC has BAC=20 \angle BAC = 20 ^\circ and ACB=75\angle ACB = 75 ^\circ . PP is a point in the interior of triangle ABCABC. Points D,ED, E and FF lie on BC,CABC, CA and ABAB, respectively, such that A,E,P,F A, E, P, F are concyclic and C,D,P,EC, D, P, E are concyclic. What is the measure (in degrees) of DPF \angle DPF ?

Details and assumptions

Points are concyclic if they lie on a circle.

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