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equal angles inside square ABCD, midpoints of BC and CD related

Source: Sharygin 2010 Final 8.6

October 2, 2018
geometryanglessquaremidpointsAngle Chasinggeometry solvedSharygin Geometry Olympiad

Problem Statement

Let E,FE, F be the midpoints of sides BC,CDBC, CD of square ABCDABCD. Lines AEAE and BFBF meet at point PP. Prove that ∠PDA=∠AED\angle PDA = \angle AED.
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