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collinear wanted, convex ABCDEF , 2 congruent rectangles

Source: 2019 NZMO Round 1 p7

January 10, 2021
geometrycollinearrectangle

Problem Statement

Let ABCDEFABCDEF be a convex hexagon containing a point PP in its interior such that PABCPABC and PDEFPDEF are congruent rectangles with PA=BC=PD=EFPA = BC = P D = EF (and AB=PC=DE=PFAB = PC = DE = PF). Let ℓ\ell be the line through the midpoint of AFAF and the circumcentre of PCDPCD. Prove that ℓ\ell passes through PP.
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