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Angles in a quadrilateral (beautiful and almost famous)

Source: Problem 4, Brazil MO 1993

March 18, 2006
trigonometrygeometrycircumcircleLaw of Sinesperpendicular bisectorBrazilian Math Olympiad

Problem Statement

ABCDABCD is a convex quadrilateral with ∠BAC=30∘\angle BAC = 30^\circ ∠CAD=20∘\angle CAD = 20^\circ∠ABD=50∘\angle ABD = 50^\circ∠DBC=30∘\angle DBC = 30^\circ If the diagonals intersect at PP, show that PC=PDPC = PD.
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