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Part of 2024 Polish Junior MO Finals

Problems(1)

A convex quadrilateral with an interior point

Source: 2024 Polish Junior Math Olympiad Finals P1

5/5/2024
Can we find a convex quadrilateral ABCDABCD with an interior point PP satisfying AB=AP,   BC=BP,   CD=CP,   \text{and}   DA=DP   ?
geometrygeometry proposedconvex quadrilateral