For example if $OP$ happened to be $2/3$ of the radius then $OP'$ would be $3/2$ of the radius.
You can use the interactivity below to help you explore how the positions of a pair of points relate to each other.Full Screen Version
Once you have a feel for that, leave the interactivity and go on to the main problem which is best done by drawing sketches on paper.
In the diagram above, $P$ and $P'$ are a connected pair, and $Q$ and $Q'$ the same, both pairs behaving like the points in the interactivity.
Now for the problem : The radius of the circle is 10 units, $OP$ is 8 units and $OQ$ is 6 units.
If the distance $PQ$ is 5 units what is the distance $P'Q'$?