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2019 Iberoamerican Mathematical Olympiad, P3

Source:

September 15, 2019
geometrycircumcircle

Problem Statement

Let Γ\Gamma be the circumcircle of triangle ABCABC. The line parallel to ACAC passing through BB meets Γ\Gamma at DD (D≠BD\neq B), and the line parallel to ABAB passing through CC intersects Γ\Gamma to EE (E≠CE\neq C). Lines ABAB and CDCD meet at PP, and lines ACAC and BEBE meet at QQ. Let MM be the midpoint of DEDE. Line AMAM meets Γ\Gamma at YY (Y≠AY\neq A) and line PQPQ at JJ. Line PQPQ intersects the circumcircle of triangle BCJBCJ at ZZ (Z≠JZ\neq J). If lines BQBQ and CPCP meet each other at XX, show that XX lies on the line YZYZ.
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