As you go along the perpendicular bisector, will the circle drawn from that point through A and B appear more curved or less curved? [Page No. 95]
It will appear less curved, that is, flatter. From the previous question, moving along the perpendicular bisector makes the radius larger, and a larger circle bends more gently. (The amount of bending, called the curvature, equals , so as the radius increases the curvature decreases.) The arc through A and B therefore looks straighter and straighter. In the extreme, as the radius tends to infinity, the arc flattens out towards the straight line AB.