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Some geometry

Source: St Petersburg Olympiad 2014, Grade 10, P5

October 26, 2017
geometry

Problem Statement

Incircle ω\omega of ABCABC touch ACAC at B1B_1. Point E,FE,F on the ω\omega such that ∠AEB1=∠B1FC=90\angle AEB_1=\angle B_1FC=90. Tangents to ω\omega at E,FE,F intersects in DD, and BB and DD are on different sides for line ACAC. MM- midpoint of ACAC. Prove, that AE,CF,DMAE,CF,DM intersects at one point.
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