MathDB

6

Part of 2019 Bulgaria National Olympiad

Problems(1)

A geometry problem

Source: Bulgaria National Olympiad 2019

4/20/2019
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.
geometrygeometric transformationreflection