IMO 1998 Problem 1

Day 1

A convex quadrilateral $ABCD$ has perpendicular diagonals. The perpendicular bisectors of the sides $AB$ and $CD$ meet at a unique point $P$ inside $ABCD$ . Prove that the quadrilateral $ABCD$ is cyclic if and only if triangles $ABP$ and $CDP$ have equal areas.

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Dataset text AI-MO AoPS. Quoted with source.

Official text: IMO 1998 official English paper, page 1.

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