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6 concyclic points given, concurrent, perpendicular, parallel wanted

Source: KJMO 2006 p3

April 30, 2019
geometryConcyclicperpendicularparallel

Problem Statement

In a circle OO, there are six points, A,B,C,D,E,FA,B,C,D,E, F in a counterclockwise order. BD⊥CFBD \perp CF, and CF,BE,ADCF,BE,AD are concurrent. Let the perpendicular from BB to ACAC be MM, and the perpendicular from DD to CECE be NN. Prove that AE//MNAE // MN.
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