As you move away from segment AB along its perpendicular bisector, do the radii of the circles containing
A and B increase or decrease?                                                                                                                                                         [Page No. 95]

The radii increase. Let O be the centre (a point on the perpendicular bisector) and M the midpoint of AB. Since $OM \perp AB$, triangle OMA is right-angled at M, so $OA^2 = OM^2 + MA^2$.

Here $MA=\frac{AB}{2}$ stays fixed, while $OM$ grows as $O$ moves away from $AB$.
Therefore $OA$, which is the radius, also grows.
So moving away from $AB$ along the perpendicular bisector makes the circles larger.