MathDB
Hard pure geometry

Source: 2019 Danube

October 29, 2019
geometrycircumcircleOrthocentre

Problem Statement

Let APD APD be an acute-angled triangle and let B,C B,C be two points on the segments (excluding their endpoints) AP,PD, AP,PD, respectively. The diagonals of ABCD ABCD meet at Q. Q. Denote by H1,H2 H_1,H_2 the orthocenters of APD,BPC, APD,BPC, respectively. The circumcircles of ABQ ABQ and CDQ CDQ intersect at X≠Q, X\neq Q, and the circumcircles of ADQ,BCQ ADQ,BCQ meet at Y≠Q. Y\neq Q. Prove that if the line H1H2 H_1H_2 passes through X, X, then it also passes through Y. Y.
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