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two angles are equal

Source: 2011-2012 china second round,problem 1

October 30, 2011
geometrycircumcirclesymmetrycyclic quadrilateralgeometry proposed

Problem Statement

Let P,QP,Q be the midpoints of diagonals AC,BDAC,BD in cyclic quadrilateral ABCDABCD. If ∠BPA=∠DPA\angle BPA=\angle DPA, prove that ∠AQB=∠CQB\angle AQB=\angle CQB.
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