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A line tangent to a circumcircle

Source: Lusophon Mathematical Olympiad 2021 Problem 3

December 19, 2021
geometrycircumcircle

Problem Statement

Let triangle ABCABC be an acute triangle with AB≠ACAB\neq AC. The bisector of BCBC intersects the lines ABAB and ACAC at points FF and EE, respectively. The circumcircle of triangle AEFAEF has center PP and intersects the circumcircle of triangle ABCABC at point DD with DD different to AA.
Prove that the line PDPD is tangent to the circumcircle of triangle ABCABC.
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