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# Cir_Angle_Theorems

Term | Definition |
---|---|

A tangent and a radius (tangent) | will be perpendicular at the point of tangency |

Tangent segments from a common external point (tangent) | are congruent |

central angle | angle with a vertex at the center |

semicircle | arc whose endpoints are a diameter |

arc | unbroken part of the circle |

minor arc | if angle ACB < 180. Will be named AB |

major arc | if angle ACB > 180. Will be named ABC |

2 minor arcs are congruent (chords) | if their chords are congruent |

One chord is a perpendicular bisector of another (chords) | the first chord is a diameter |

diameter | chord that passes through the center of the circle |

chord | segment that has endpoints on the edge of a circle |

2 chords are congruent (chords) | if they are equal distance from the center |

inscribed angle | an angle whose vertex is on a circle and whose sides contain chords |

measure of an inscribed angle (inscribed angles) | 1/2 the measure of the intercepted arc |

2 inscribed angles intercept the same arc (inscribed angles) | the angles are congruent |

an inscribed angle is a right angle (inscribed angles) | hypotenuse is the diameter of the circle |

an inscribed quadrilateral (inscribed angles) | opposite angles are supplementary |

tangent and chord intersect at a point | the measure of each angle is half of its intercepted arc |

2 chords intersect inside a circle (angles) | measure of each angle is half the sum (+) of the arcs intercepted by the angle and its vertical angle |

tangent and a secant, 2 tangents, or 2 secants intersect outside a circle | the measure the the angle formed is half the difference (-) of the measures of the intercepted arcs. |

2 chords intersect inside a circle (length) | product (x) of the lengths of the segments of one chord equals the product of the lengths of the other |

2 secant segments share the same endpoint outside the circle (length) | the product (x) of the lengths of one entire secant and its external segment equals the product of the length of the other secant and its outside segment |

a secant segment and a tangent segment share an outside endpoint (length) | product (x) of the lengths of the entire secant and its outside segment equals the length of the tangent segment squared |

circumference (length) | distance around a circle (pi * 2r) or (pi * d) |

circumference (degrees) | 360- The ratio of the arc to the circumference equals the ratio of the angle to 360 |