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# Adv. Circle Terms

### Secant, chord, isoparametric theorem, etc.

Shape/Term | Definition | Formula |
---|---|---|

Circle | the set of all points that are the same distance from a fixed point G | C=תּd A=תּr² |

Pi | The ratio of the circumference to the diameter of any circle | תּ=C∕d |

Radius | The distance from the center to the points on the circle | (radius-n/a) |

Diameter | A line segment drawn through the center of a circle with both endpoints on the circle | d=2r |

Chord | a segment with both endpoints on the circle | (chord-n/a) |

Tangent | a line that touches the circle in one point | (tangent-n/a) |

Secant | A line extended from the ends of a chord | (secant-n/a) |

Central Angle | an angle with its vertex in the center of the circle | m(central angle)=m(intercepted minor arc) |

Major Arc | the arc that is "outside" a central angle; more than 180 degrees | m(major arc)=360-m(minor arc) |

Minor Arc | the arc "within" an angle | (minor arc-n/a) |

Concentric Circles | circles that share a center (like a target) | A(area between concentric circles)=A(larger circle)-A(smaller circle) |

Inscribed Angle | an angle with its vertex on the circle and whose sides intersect the circle | m(Inscribed angle)=(1∕2)m(intercepted arc) |

Intercepted Arc | The arc "trapped inside" an inscribed or central angle | (intercepted arc-n/a) |

Semicircle | The endpoints of any diameter divide a circle into two congruent arcs; each arc is called a _____ | m(semicircle)=180 degrees |

Tangent/Radius Theorem | Any tangent of a circle is perpendicular to a radius of the circle where they intersect | m(angle between tangent and touching radius)=90 degrees |

Diameter/Chord Theorem | If a diameter bisects a chord, then it is perpendicular to the chord/vice versa | If diameter bisects chord AB at C, then AB=AC and all angles are 90 degrees |

Diameter Right Angle Theorem | Any angle inscribed to catch a 180 degree angle is a right angle. | (diameter right angle theorem-n/a) |

Volume of a Prism/Cylinder | Volume of a prism is the base area times the height. | V=Bh |

Volume of a Pyramid/Cone | Volume of a Pyramid/cone is one third of the base area times the height | V=1∕3 Bh |

Oblique Pyramid/Prism | Pyramids wth the vertex not directly above the center of the base | Same as for right pyramid/prism |

Area of a Segment | The area between a chord and the circle | A(segment)=A(sector)-A("wedged" triangle) |

Isoparametric Theorem | For a given perimeter, the shape with the most area is a circle | (isoparametric theorem-n/a) |

Sector | The pie-shaped wedge defined by a central angle and its arc | A(sector)=A(circle)∙(m(angle/arc)∕360 degrees) |

Created by:
orngjce223