# Apollonius’ circle

Apollonius’ circle.
The locus of a point moving so that the ratio of its distances^{} from two fixed points is fixed, is a circle.

If two circles ${C}_{1}$ and ${C}_{2}$ are fixed with radii ${r}_{1}$ and ${r}_{2}$, then the circle of Apollonius of the two centers with ratio ${r}_{1}/{r}_{2}$ is the circle whose diameter^{} is the segment that the two homothety centers of the circles.

Title | Apollonius’ circle |
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Canonical name | ApolloniusCircle |

Date of creation | 2013-03-22 11:44:22 |

Last modified on | 2013-03-22 11:44:22 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 11 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 51-00 |

Classification | msc 35-01 |

Related topic | HarmonicDivision |