Question 2
In a circle $C$ with centre $O$ and radius $r$, let $C_1,C_2$ have centres $O_1,O_2$ and radii $r_1,r_2$. Each $C_i$ is internally tangent to $C$ at $A_i$, and $C_1,C_2$ are externally tangent at $A$. Prove that the lines $OA,O_1A_2,O_2A_1$ are concurrent.
Editorial qualification (AI): assume $A\ne O$, so the line $OA$ is defined. The printed problem omits this qualification; the exceptional configuration is explained below.
Editorial qualification (AI): assume $A\ne O$, so the line $OA$ is defined. The printed problem omits this qualification; the exceptional configuration is explained below.