# Comb + Geo = Tension

Geometry Level 5

Let $$ABC$$ be a triangle with $$AB = AC$$. The angle bisectors of $$A$$ and $$B$$ meet the sides $$BC$$ and $$AC$$ in $$D$$ and $$E$$, respectively. Let $$K$$ be the incenter of the triangle $$ADC$$. Suppose that $$\angle BEK= \dfrac{\pi}{4}$$. Find sum of all possible values of $$\angle BAC$$.

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