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dutch angle chasing for TST, 2 circles and angle bisector related

Source: 2015 Dutch BxMO / EGMO TST p4

September 19, 2018
geometrycircumcircleequal anglesAngle Chasingangle bisector

Problem Statement

In a triangle ABCABC the point DD is the intersection of the interior angle bisector of ∠BAC\angle BAC and side BCBC. Let PP be the second intersection point of the exterior angle bisector of ∠BAC\angle BAC with the circumcircle of ∠ABC\angle ABC. A circle through AA and PP intersects line segment BPBP internally in EE and line segment CPCP internally in FF. Prove that ∠DEP=∠DFP\angle DEP = \angle DFP.
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