Meaning of circle of Apollonius | Babel Free

Definitions

1. The figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, =/(\frac).
2. Any of eight circles (including degenerate cases) that, for a given set of three circles, solve the problem of Apollonius (i.e., intersect each circle tangentially).

Examples

“In the present⟳ paper an attempt⟳ is made to find⟳ for the tetrahedron the analogues of the circles of Apollonius of the triangle.”

“It follows that O lies on the circle of Apollonius for A and C and ratio OT/OC, and on the circle of Apollonius for B and C and ratio OT/OC. Point⟳ O is thus found at the intersections, if any exist⟳, of these two circles of Apollonius. The details are left to the reader.”

“More generally, the locus of points z such that #92;left#92;vertx-z#92;right#92;vert#61;#92;alpha#92;left#92;verty-z#92;right#92;vert is a circle of Apollonius which has x and y as inverse points and which cuts each circle through x and y orthogonally.[…]They show⟳ loci analogous to circles of Apollonius and the locus of points equidistant from two given points when the norm is an #92;mathcal#123;l#125;#95;p-norm.”

CEFR level