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2004 IMO Problems/Problem 5

Revision as of 11:27, 23 August 2020 by Pureswag (talk | contribs) (Created page with "In a convex quadrilateral <math>ABCD</math>, the diagonal <math>BD</math> bisects neither the angle <math>ABC</math> nor the angle <math>CDA</math>. The point <math>P</math> l...")
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In a convex quadrilateral $ABCD$, the diagonal $BD$ bisects neither the angle $ABC$ nor the angle $CDA$. The point $P$ lies inside $ABCD$ and satisfies \[\angle PBC = \angle DBA \text{ and } \angle PDC = \angle BDA.\]

Prove that $ABCD$ is a cyclic quadrilateral if and only if $AP = CP.$

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