Question 160
Let $\triangle ABC$ be a triangle with $AB = AC$. The angle bisectors of $\angle CAB$ and $\angle ABC$ meet the sides $BC$ and $CA$ at $D$ and $E$, respectively. Let $K$ be the incenter of triangle $ADC$. Suppose that $\angle BEK = 45^\circ$. Find all possible values of $\angle CAB$.
(This problem was suggested by Peter Vandendriessche and Jan Vonk from Belgium and by Hojoo Lee from South Korea.)
(This problem was suggested by Peter Vandendriessche and Jan Vonk from Belgium and by Hojoo Lee from South Korea.)