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concurrency related to symmetric wrt side midpoints

Source: Germany Federal - Bundeswettbewerb Mathematik 2009, round 1, p3

April 9, 2020
geometryconcurrencyconcurrentmidpointsSymmetric

Problem Statement

Let PP be a point inside the triangle ABCABC and Pa,Pb,PcP_a, P_b ,P_c be the symmetric points wrt the midpoints of the sides BC,CA,ABBC, CA,AB respectively. Prove that that the lines APa,BPbAP_a, BP_b and CPcCP_c are concurrent.
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