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angle chasing , <BAC = 60^o , 2 < BAE = <ACB

Source: Switzerland - Swiss MO 2016 p1

July 15, 2020
anglesgeometryequal anglescircumcircle

Problem Statement

Let ABCABC be a triangle with ∠BAC=60o\angle BAC = 60^o. Let EE be the point on the side BCBC , such that 2∠BAE=∠ACB2 \angle BAE = \angle ACB . Let DD be the second intersection of ABAB and the circumcircle of the triangle AECAEC and PP be the second intersection of CDCD and the circumcircle of the triangle DBEDBE. Calculate the angle ∠BAP\angle BAP.
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