1998 IMO Problems/Problem 1

Problem

In the convex quadrilateral $ABCD$ , the diagonals $AC$ and $BD$ are perpendicular and the opposite sides $AB$ and $DC$ are not parallel. Suppose that the point $P$ , where the perpendicular bisectors of $AB$ and $DC$ meet, is inside $ABCD$ . Prove that $ABCD$ is a cyclic quadrilateral if and only if the triangles $ABP$ and $CDP$ have equal areas.

Solution

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1998 IMO (Problems) • Resources
Preceded by First Question	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 2
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1998 IMO Problems/Problem 1

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