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Cyclic hexagon prove equal segments

Source: China Team Selection Test 2016 Test 1 Day 1 Q1

March 16, 2016
geometry

Problem Statement

ABCDEFABCDEF is a cyclic hexagon with AB=BC=CD=DEAB=BC=CD=DE. KK is a point on segment AEAE satisfying ∠BKC=∠KFE,∠CKD=∠KFA\angle BKC=\angle KFE, \angle CKD = \angle KFA. Prove that KC=KFKC=KF.
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