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AL, BM, CN concurrent and each bisect any other, 3 parallelograms

Source: Netherlands - Dutch NMO 1976 p2

January 27, 2023
concurrencyconcurrentgeometryparallelogram

Problem Statement

Given △ABC\vartriangle ABC and a point PP inside that triangle. The parallelograms CPBLCPBL, APCMAPCM and BPANBPAN are constructed. Prove that ALAL, BMBM and CNCN pass through one point SS, and that SS is the midpoint of ALAL, BMBM and CNCN.
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