SHARYGIN 2009 Problem 1

Points $B_1$ and $B_2$ lie on ray $AM$, and points $C_1$ and $C_2$ lie on ray $AK$. The circle with center $O$ is inscribed into triangles $AB_1C_1$ and $AB_2C_2$. Prove that the angles $B_1OB_2$ and $C_1OC_2$ are equal.