**8.3 Common Tangents**

A

**common tangent**to two circles is a straight line that touches each of the circles at only one point.**1. Intersect at two points**

**(a) Circles of the same size**

Number of common tangents |
Properties of common tangents |

Two common tangents:AB and CD |
AC = BDAB = CDAB parallel to // OR parallel to // CD |

**(b) Circles of different sizes**

Number of common tangents |
Properties of common tangents |

Two common tangents:ABE and CDE |
AB = CDBE = DEOA // RB OC // RD |

**2. Intersect at one point**

**(a) Circles of the same size**

Number of common tangents |
Properties of common tangents |

Three common tangents:AB, CD and PQ |
AC = PQ = BDAB = OR = CDAB // OR // CDAC // PQ // BDPQ perpendicular to OR |

**(b) Circles of different sizes**

**(i) External contact**

Number of common tangents |
Properties of common tangents |

Three common tangents:ABE, CDE and PQ |
AB = CDBE = DEOA // RB OC // RDPQ perpendicular to ORE |

**(ii) Internal contact**

Number of common tangents |
Properties of common tangents |

One common tangent: PQR |
ONQ perpendicular to PR |

**3. Do not intersect**

**(a) Circles of the same size**

Number of common tangents |
Properties of common tangents |

Four common tangents:
AB, CD, PS and RQ |
AB = CD = OVPS = RQ AB // OV // CD |

**(b) Circles of different sizes**

Number of common tangents |
Properties of common tangents |

Four common tangents:
AB, CD, PS and RQ |
AB = CDBT = DTPS = RQ OA // VBOC // VD |