ConicsAndSimilarities2

Conics and similarities of circles II

File CirclesSimilar.html contains a short discussion on the locus of points which serve as similarity centers F of some similarity S mapping a circle (d) to another circle (d'). In file ConicsAndSimilarities.html it is shown that, for such a similarity, line EE' joining a point E on (d) with E'=S(E) on (d') envelopes a conic with one focus at F and tangent (under certain conditions) to the two given circles (d) and (d').
The example below is a case where the two circles (d) and (d') are not tangent to the conic (blue ellipse) generated by the above recipe.

Points {V,W} are the homothety centers of the two circles (d) and (d'). Circle (f) has these two points as diametral points. F is always on this circle. The resulting conic for such a configuration, where one of the circles (d') is totally inside the other, is always an ellipse. The ellipse may contact or not the smaller circle (d').
A clue for the behavior of the ellipse regarding its contact with circle (d') may give the picture contained in DistanceFunction.html .

Conics and similarities of circles II

See Also