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Circumference with diameter HG

Source: Problem 6, Brazilian MO 2015

October 20, 2015
geometry proposedgeometrycircumcircle

Problem Statement

Let △ABC\triangle ABC be a scalene triangle and XX, YY and ZZ be points on the lines BCBC, ACAC and ABAB, respectively, such that ∡AXB=∡BYC=∡CZA\measuredangle AXB = \measuredangle BYC = \measuredangle CZA. The circumcircles of BXZBXZ and CXYCXY intersect at PP. Prove that PP is on the circumference which diameter has ends in the ortocenter HH and in the baricenter GG of △ABC\triangle ABC.
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