The Line Segment joining two points on a curve. The term is often used to describe a Line Segment whose ends lie on a Circle. In the above figure, is the Radius of the Circle, is called the Apothem, and the Sagitta.

The shaded region in the left figure is called a Sector, and the shaded region in the right figure is called a Segment.

All Angles inscribed in a Circle and subtended by the same chord are equal. The converse is also true: The Locus of all points from which a given segment subtends equal Angles is a Circle.

Let a Circle of Radius have a Chord at distance . The Area enclosed by the Chord, shown
as the shaded region in the above figure, is then

(1) |

(2) |

(3) |

(4) |

Checking the limits, when , and when ,

(5) |

© 1996-9

1999-05-26