Let the radius of $R$'s track be $r$ and let the radius of the first semicircle of $P$'s track be $p$; then the radius of the second circle of this track is $r-p$.

The total length of $P$'s track is $\pi p+\pi (r-p)=\pi r$, the same length as $R$'s track.

By a similar argument, the length of $Q$'s track is also $\pi r$.