Question 60
Given a scalene triangle $ABC$. On the rays $AC \rightarrow$ and $BC \rightarrow$, the points $C_a$ and $C_b$ are chosen, respectively, such that $AC_a = BC_b = AB$. We denote by $O_c$ the center of the circumcircle about $\triangle CC_a C_b$. Analogously, we define the points $O_a$ and $O_b$. Prove that the lines $AO_a$, $BO_b$ and $CO_c$ intersect at a point that lies on the circumcircle of the triangle $ABC$.
(Alexander Ivanov)
(Alexander Ivanov)