Question 113
A triangle $ABC$ with obtuse angle at $C$ is given. Axis $o_1$ of side $AC$ intersects side $AB$ in point $K$, axis $o_2$ of side $BC$ intersects side $AB$ in point $L$. Denote $O$ intersection of the axes $o_1$ and $o_2$. Prove that centre of the incircle of triangle $KLC$ lies on the circumcircle of triangle $OKL$.