[ [MT - line or segment]

Two wheels of radii $r_{1}$ and $r_{2}$ roll along a line $l$. Find the set of points of intersection $M$ of their common internal tangents.

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Let $O_{1}$ and $O_{2}$ be the centers of wheels with radii $r_{1}$ and $r_{2}$ respectively. If $M$ is the point of intersection of the internal tangents, then $O_{1} M: O_{2} M=r_{1}: r_{2}$. From this condition, it is easy to obtain that the distance from point $M$ to line $l$ is $2 r_{1} r_{2} /\left(r_{1}+r_{2}\right)$. Therefore, all points of intersection of the common internal tangents lie on a line parallel to line $l$ and at a distance of $2 r_{1} r_{2} /\left(r_{1}+r_{2}\right)$ from it.