2009 IMO Problems/Problem 4


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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