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prove that CPQ is equilateral if ABC triangle has <C=60^o

Source: Rioplatense Olympiad 2002 level 3 P3

September 6, 2018
geometryEquilateral Triangle

Problem Statement

Let ABCABC be a triangle with ∠C=60o\angle C=60^o. The point PP is the symmetric of AA with respect to the point of tangency of the circle inscribed with the side BCBC . Show that if the perpendicular bisector of the CPCP segment intersects the line containing the angle - bisector of ∠B\angle B at the point QQ, then the triangle CPQCPQ is equilateral.
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