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Inscribed quadrilateral (again)

Source: St Petersburg 2008 10th grade #5

July 28, 2011
geometrycyclic quadrilateralgeometry proposed

Problem Statement

In cyclic quadrilateral ABCDABCD rays ABAB and DCDC intersect at point EE, while segments ACAC and BDBD intersect at FF. Point PP is on ray EFEF such that angles BPEBPE and CPECPE are congruent. Prove that angles APBAPB and DPCDPC are also equal.
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