Let ABCD be a convex quadrilateral, I1 and I? be the incenters of ?ABC and...

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Let ABCD be a convex quadrilateral, I1 and I? be the incenters of ?ABC and ?DBC respectively. The line I1I? intersects the lines AB and DC at the points E and F respectively. Suppose lines ABand DC intersect at P, and PE = PF. Prove that the points A, B, C, D are concyclic.

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