Three lines passing through point $ O$ form equal angles by pairs. Points $ A_1$, $ A_2$ on the first line and $ B_1$, $ B_2$ on the second line are such that the common point $ C_1$ of $ A_1B_1$ and $ A_2B_2$ lies on the third line. Let $ C_2$ be the common point of $ A_1B_2$ and $ A_2B_1$. Prove that angle $ C_1OC_2$ is right.