IMO Problem 7

Geometry Level pending

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.

This problem is from the IMO.This problem is from the IMO.This problem is part of this set.

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