IMO 1983 LL USA65

Let ABCD be a convex quadrilateral whose diagonals AC and

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IMO 1983 LL USA65

Origin: USA

Problem

Let ABCD be a convex quadrilateral whose diagonals AC and BD intersect in a point P. Prove that AP PC = cot \angleBAC + cot \angleDAC cot \angleBCA + cot \angleDCA.