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2019 IGO Intermediate P4

Source: 6th Iranian Geometry Olympiad (Intermediate) P4

September 20, 2019
IGOIrangeometry

Problem Statement

Let ABCDABCD be a parallelogram and let KK be a point on line ADAD such that BK=ABBK=AB. Suppose that PP is an arbitrary point on ABAB, and the perpendicular bisector of PCPC intersects the circumcircle of triangle APDAPD at points XX, YY. Prove that the circumcircle of triangle ABKABK passes through the orthocenter of triangle AXYAXY.
Proposed by Iman Maghsoudi
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