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Puerto Rico IBERO TST Problem 4

Source:

August 15, 2011
geometrycircumcirclepower of a pointradical axis

Problem Statement

Let PP be a point inside the triangle ABCABC, such that the angles ∠CBP\angle CBP and ∠PAC\angle PAC are equal. Denote the intersection of the line APAP and the segment BCBC by DD, and the intersection of the line BPBP with the segment ACAC by EE. The circumcircles of the triangles ADCADC and BECBEC meet at CC and FF. Show that the line CPCP bisects the angle DFEDFE.
Please remember to hide your solution. (by using the hide tags of course.. I don't literally mean that you should hide it :ninja: )
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