IMO Problem 7

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

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