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Angle is twice of another

Source: China Second Round 2015 (A) Q3

May 5, 2016
geometrycircumcircle

Problem Statement

PP is a point on arc \overarc{BC} of the circumcircle of △ABC\triangle ABC not containing AA, KK lies on segment APAP such that BKBK bisects ∠ABC\angle ABC. The circumcircle of △KPC\triangle KPC meets AC,BDAC,BD at D,ED,E respectively. PEPE meets ABAB at FF. Prove that ∠ABC=2∠FCB\angle ABC=2\angle FCB.
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