IMO Shortlist 2018 problem G2


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3. listopada 2019.
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Let ABC be a triangle with AB=AC, and let M be the midpoint of BC. Let P be a point such that PB<PC and PA is parallel to BC. Let X and Y be points on the lines PB and PC, respectively, so that B lies on the segment PX, C lies on the segment PY, and \angle PXM=\angle PYM. Prove that the quadrilateral APXY is cyclic.

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