IMO Shortlist 2018 problem G1


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3. listopada 2019.
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Let \Gamma be the circumcircle of acute triangle ABC. Points D and E are on segments AB and AC respectively such that AD = AE. The perpendicular bisectors of BD and CE intersect minor arcs AB and AC of \Gamma at points F and G respectively. Prove that lines DE and FG are either parallel or they are the same line.

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf