2009 IMO Problems/Problem 4

Problem

Let $ABC$ be a triangle with $AB=AC$ . The angle bisectors of $\angle CAB$ and $\angle ABC$ meet the sides $BC$ and $CA$ at $D$ and $E$ , respectively. Let $K$ be the incentre of triangle $ADC$ . Suppose that $\angle BEK=45^\circ$ . Find all possible values of $\angle CAB$ .

Authors: Jan Vonk and Peter Vandendriessche, Belgium, and Hojoo Lee, South Korea

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2009 IMO Problems/Problem 4

Problem