Two Concyclic Quadruples

Geometry Level 3

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

Details and assumptions

Points are concyclic if they lie on a circle.

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