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circle of Apollonius

circle of Apollonius noun: the figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, =/(\frac).

circle of apollonius: the figure (a generalised circle) definable as the locus of points P such that, for given points A,...
Image: Limaner, Public domain, via Wikimedia Commons

Noun

circle of Apollonius (plural circles of Apollonius)

  1. The figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, =/(\frac).
    • In the present paper an attempt is made to find for the tetrahedron the analogues of the circles of Apollonius of the triangle.1934, Tôhoku Mathematical Journal, volumes 39-40, page 264
    • 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.1995, Howard Whitley Eves, College Geometry, page 165
  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).

Forms of circle of Apollonius

pluralcircles of Apollonius

Origin of circle of Apollonius

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

Questions about circle of Apollonius

What does circle of Apollonius mean?
Circle of Apollonius means the figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, =/(\frac).
What part of speech is circle of Apollonius?
Circle of Apollonius is a noun.
What is the plural of circle of Apollonius?
The plural of circle of Apollonius is circles of Apollonius.

Words near circle of Apollonius in the dictionary

  1. circle lens
  2. circle lenses
  3. circle marriage
  4. circle marriages
  5. circle of antisimilitude
  6. circle of Apollonius
  7. circle of confusion
  8. circle of fifths
  9. circle of friends
  10. circle of life
  11. circle of the gorge

Source and license

Adapted from Wiktionary: circle of Apollonius (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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