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Drawn through the incenter I of the triangle

Source: IMO ShortList 1991, Problem 5 (SPA 4)

August 15, 2008
geometryincentertrigonometrytrig identitiesLaw of SinesIMO Shortlist

Problem Statement

In the triangle ABC, ABC, with \angle A \equal{} 60 ^{\circ}, a parallel IF IF to AC AC is drawn through the incenter I I of the triangle, where F F lies on the side AB. AB. The point P P on the side BC BC is such that 3BP \equal{} BC. Show that \angle BFP \equal{} \frac{\angle B}{2}.
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