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# Circles

### Theorems and definitions

Question | Answer |
---|---|

Circle | set of all points in a place that are equidistant from a given point called the center of the circle |

Chord | a segment whose endpoints are points on the circle (inside) |

Secant | a line that intersects a circle in two points (outside) |

Tangent | a line that intersects a circle in exactly one point |

concentric | coplanar circles that have a common center |

common tangent | a line or segment that is tangent to two coplanar circles |

point of tangency | the point at which a tangent line intersects the circle to which it is tangent |

Theorem 1 | if a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency |

Theorem 2 | in a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle |

theorem 3 | if two segments from the same exterior point are tangent to a circle, then they are congruent |

central angle | an angle whose vertex is the center of the circle |

minor arc | part of a circle that measures less that 180; named with two letters |

Major Arc | part of a circle that measures between 180 and 360; named with three letters |

Semicircle | an arc whose endpoints are the endpoints of a diameter of the circle |

Measure of a Minor Arc | the measure of its central angle |

Measure of a Major Arc | the difference between 360 and the measure of its associated minor arc |

Congruent Arc | two arcs of the same circle or of congruent circles that have the same measures |

Arc Addition Postulate | the measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs |

Theorem 4 | in the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent |

Theorem 5 | If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc |

Theorem 6 | If one chord is a perpendicular bisector of another chord, then the first chord is a diameter |

Theorem 7 | In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center |

Created by:
McChicklet