 Collinearity for tangent circles between parallel lines

Let two positive-radius circles have external tangency at $Q$ and lie in the closed strip between two parallel lines, touching opposite boundaries at $P,R$. Then $P,Q,R$ are collinear. To prove this, choose coordinates with the boundaries $x=0,d$, put $P=(0,0)$ and $R=(d,h)$, and write the centres as $O_1=(r_1,0)$, $O_2=(d-r_2,h)$. The contact point isThe closed line segment $PR$ is contained in the union of the two closed disks: its portions from $P$ to $Q$ and from $Q$ to $R$ are chords. The strip and external tangency hypotheses are essential to this particular formulation.