InvertCircleSeventeen points on a circle are paired by segments to 17 points on another circle. In fact, each point is the inverse of its mate in the circle (O,Z), and each of the two circles is the inverse of the other in the circle (O,Z).
The point X determines the ratio |AX|/|AB|. This ratio is used to dilate the 17 points to a set of 17 intermediate points, which are linked by blue segments and reflected in segment AB. When X is animated, the linkage moves between the two circles, representing a "slow motion inversion" of one circle into the other.
Be sure to drag C and D so that pairs of circles overlap.
For more, see GEOMETRY IN ACTION, Chapter 3.