Points $X_1$ and $X_2$ move along fixed circles with centers $O_1$ and $O_2$, respectively, so that $O_1X_1 \parallel O_2X_2$. Find the locus of the intersection point of lines $O_1X_2$ and $O_2X_1$.
Source: Oral Moscow geometry olympiad 2023 10-11.2
Tags: geometry
Points $X_1$ and $X_2$ move along fixed circles with centers $O_1$ and $O_2$, respectively, so that $O_1X_1 \parallel O_2X_2$. Find the locus of the intersection point of lines $O_1X_2$ and $O_2X_1$.
