$OM$ and $ON$ lines are perpendicular if and only if the $S$, $N$ and $T$ points are collinear

Question

A circle with the center in $O$ is tangent inside two secant circles located inside it. If $S$ and $T$ are the tangent points and $M$ and $N$ are the intersection points of the two circles, with $N$ being closer to the right $ST$ than $M$, prove that the $OM$ and $ON$ lines are perpendicular if and only if the $S$, $N$ and $T$ points are collinear. We have shown that if the points are collinear then we have the perpendicular lines but I do not know each other. How should I start?