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A geometry problem

Source: Bulgaria National Olympiad 2019

April 20, 2019
geometrygeometric transformationreflection

Problem Statement

Let ABCDEFABCDEF be an inscribed hexagon with AB.CD.EF=BC.DE.FAAB.CD.EF=BC.DE.FA
Let B1B_1 be the reflection point of BB with respect to ACAC and D1D_1 be the reflection point of DD with respect to CE,CE, and finally let F1F_1 be the reflection point of FF with respect to AE.AE. Prove that △B1D1F1∼BDF.\triangle B_1D_1F_1\sim BDF.
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