Question 99
Let $I$ be the center of inscribed circle of the non-isosceles triangle $ABC$. The ray $AI$ meets circumscribed circle of the triangle $ABC$ at point $D$. The circle passing through $C$, $D$, and $I$ meets again the ray $BI$ at point $K$.
Prove that $BK = CK$.
Prove that $BK = CK$.