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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