Comb + Geo = Tension

Geometry Level 5

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


The answer is 150.

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