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# Circles

### postulates and theorems relating to circles (chp. 10)

Hypothesis | Conclusion |
---|---|

Two arcs are congruent if and only if | their corresponding central angles are congruent |

The measure of an arc formed by two adjacent arcs is | the sum of the measures of the two arcs |

In a circle or in congruent circles, two minor arcs are congruent if and only if | their corresponding chords are congruent |

In a circle, if the diameter (or radius) is perpendicular to a chord | then it besects the chord and its arc |

In a circle or in congruent cirlces, two chords are congruent if and only if | they are quidistant from the center |

If an angle is inscribed in a circle, | then the measure of the angle equals one-half the measure of its intercepted arc ( or the measure of the intercepted arc is twice the measure of the inscribed angle) |

If two inscribed angles of a circle (or congruent circles) intercept congruent arcs (or the same arc), | then the angles are congruent |

If an inscribed angle intercepts a semicircle, | the angle is a right angle |

If a quadrilateral is inscribed in a circle, | then its opposite angles are supplementary |

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

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 |

If two segments from the same exterior point are tangent to a circle | then they are congruent |

If two secants intersect in the interior of a circle | then the measure of an angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle |

If a secant and a tangent intersect at the point of tangency | then the measure of each angle formed is one-half the measure of its intercepted arc |

If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, | then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs |

If two chords intersect in a circle, | then the products of the measures of the segments of the chords are equal |

If two secent segments are drawn to a circle from an exterior point, | then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment |

If a tangent segment and a secant are drawn to a circle from an exterior point, | then the square of the measure of a tangent segment is equal to the product of the measures of the secant segment and its external secant segment |

Created by:
m.meyer