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AE // MN wanted, starting with cyclic hexagon

Source: 2021 Saudi Arabia JBMO TST 1.2

September 4, 2021
geometryhexagonCyclic

Problem Statement

In a circle OO, there are six points, A A, B B, CC, DD, EE, FF in a counterclockwise order such that BD⊥CFBD \perp CF , and CFCF, BEBE, ADAD are concurrent. Let the perpendicular from BB to ACAC be MM, and the perpendicular from DD to CECE be NN. Prove that AE∥MNAE \parallel MN.
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