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Trapezium, circles, and proving parallel lines

Source: Mexico National Olympiad Mock Exam 2018 Problem 1

November 6, 2018
geometrytrapezoidcircumcircleparallel

Problem Statement

Let ABCDABCD be a trapezoid with bases ADAD and BCBC, and let MM be the midpoint of CDCD. The circumcircle of triangle BCMBCM meets ACAC and BDBD again at EE and FF, with EE and FF distinct, and line EFEF meets the circumcircle of triangle AEMAEM again at PP. Prove that CPCP is parallel to BDBD.
Proposed by Ariel García
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