IMO Shortlist 2007 problem G7


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2. travnja 2012.
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Given an acute triangle ABC with \angle B > \angle C. Point I is the incenter, and R the circumradius. Point D is the foot of the altitude from vertex A. Point K lies on line AD such that AK = 2R, and D separates A and K. Lines DI and KI meet sides AC and BC at E,F respectively. Let IE = IF.

Prove that \angle B\leq 3\angle C.

Author: Davoud Vakili, Iran
Izvor: Međunarodna matematička olimpijada, shortlist 2007