circle of Apollonius

Meaning

Noun

• The figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, $\backslash frac\{|AP|\}\{|BP|\}\; =\; \backslash frac\{|AC|\}\{|BC|\}$.
• 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).

Origin

• Named for the ancient Greek geometer and astronomer Apollonius of Perga (ca 262—ca 190 BCE).