Question 135
Non-isosceles triangle $ABC$ is given, in which $2AC = AB + BC$. Let $I$ be the incenter of the inscribed circle in $ABC$, $K$ be the midpoint of the arc $ABC$ of the circumscribed circle. Let $T$ be such point on the line $AC$ that $\angle TIB = 90^\circ$. Prove that line $TB$ is tangent to the circumcircle of $\triangle KBI$.