Consider three pairwise intersecting circles $\omega_1$, $\omega_2$ and $\omega_3$. Let their three common chords intersect at point $R$. We denote by $O_1$ the center of the circumcircle of a triangle formed by some triple common points of $\omega_1$ & $\omega_2$, $\omega_2$ & $\omega_3$ and $\omega_3$ & $\omega_1$. and we denote by $O_2$ the center of the circumcircle of the triangle formed by the second intersection points of the same pairs of circles. Prove that points $R$, $O_1$ and $O_2$ are collinear.