Center-circles and Their Chains: What Are They?
A Mathematical Droodle
|What if applet does not run?|
Three lines (in general position) intersect in 3 points; there is 1 circumcircle passing through all three. Out of four lines one can select four triples of lines. The 4 circumcircles meet at a point (Miquel's point) and their centers lie on a circle (Steiner's circle). Five lines contain five quadruples of lines; the centers of their Steiner circles lie on a circle (Kantor's circle.) The general term for all those circles is a center-circle. For 6 lines, there are six sets of 5 lines and 6 center-circles whose centers lie on a circle. Etc.
Copyright © 1996-2018 Alexander Bogomolny