Circle of Apollonius
English
Etymology
Named for the ancient Greek geometer and astronomer Template:W (ca 262—ca 190 BCE).
Noun
- Template:Label The figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, .
- Template:Label Any of eight circles (including degenerate cases) that, for a given set of three circles, solve the Template:W (i.e., intersect each circle tangentially).
Usage notes
Template:Sense In explanations of the construction, C is sometimes shown as collinearly between A and B, but this is merely a convenience of explanation. The figure will, however, always intersect the segment at a single point. In most cases the locus of P is a circle, but in the case that C is the midpoint of AB, the result is the line perpendicular to the segment at C, thus justifying the use of the term Template:M.
The three circles of Apollonius of a triangle are the three such figures obtainable by letting AB be one of the sides of the triangle and C be the vertex opposite.