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projective candidate, lines AB, CD , FG are either parallel or concurrent.

Source: 2018 Romania JBMO TST 4.3

June 1, 2020
cyclic quadrilateralgeometryconcurrencyparallelcircumcircle

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. The line parallel to BDBD passing through AA meets the line parallel to ACAC passing through BB at EE. The circumcircle of triangle ABEABE meets the lines ECEC and EDED, again, at FF and GG, respectively. Prove that the lines AB,CDAB, CD and FGFG are either parallel or concurrent.
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