# Circle Corner

- Circle corner (a two-dimensional figure) is a right triangle having acute vertices on a circle with the hypotenuse outside the circle.
- Chord is a line segment on the interior of a circle.
- Segment of a circle is an interior part of a circle bound by a chord and an arc.

## area of a Circle Corner formula |
||

\(\large{ A = \frac{a\;b \;-\; r \; L \;+\; c \; \left(r \;-\; h\right) }{2 } }\) | ||

Symbol |
English |
Metric |

\(\large{ A }\) = area | \(\large{ft^2}\) | \(\large{m^2}\) |

\(\large{ L }\) = arc length | \(\large{ft}\) | \(\large{m}\) |

\(\large{ c }\) = chord length | \(\large{ft}\) | \(\large{m}\) |

\(\large{ a, b }\) = edge | \(\large{ft}\) | \(\large{m}\) |

\(\large{ r }\) = radius | \(\large{ft}\) | \(\large{m}\) |

\(\large{ h }\) = segment height | \(\large{ft}\) | \(\large{m}\) |

## Arc Length of a Circle Corner formula |
||

\(\large{ L = r \; \Delta }\) | ||

Symbol |
English |
Metric |

\(\large{ L }\) = arc length | \(\large{ft}\) | \(\large{m}\) |

\(\large{ \Delta }\) = angle | \(\large{deg}\) | \(\large{rad}\) |

\(\large{ r }\) = radius | \(\large{ft}\) | \(\large{m}\) |

## Chord Length of a Circle Corner formula |
||

\(\large{ c = a^2 \; b^2 }\) | ||

Symbol |
English |
Metric |

\(\large{ c }\) = chord length | \(\large{ft}\) | \(\large{m}\) |

\(\large{ a, b }\) = edge | \(\large{ft}\) | \(\large{m}\) |

## Height of a Circle Corner formula |
||

\(\large{ h = r \; \left( 1 - cos \; \frac{\Delta}{2} \right) }\) | ||

Symbol |
English |
Metric |

\(\large{ h }\) = segment height | \(\large{ft}\) | \(\large{m}\) |

\(\large{ \Delta }\) = segment angle | \(\large{deg}\) | \(\large{rad}\) |

\(\large{ r }\) = radius | \(\large{ft}\) | \(\large{m}\) |

## Perimeter of a Circle Corner formula |
||

\(\large{ p = a + b + L }\) | ||

Symbol |
English |
Metric |

\(\large{ p }\) = perimeter | \(\large{ft}\) | \(\large{m}\) |

\(\large{ L }\) = arc length | \(\large{ft}\) | \(\large{m}\) |

\(\large{ a, b }\) = edge | \(\large{ft}\) | \(\large{m}\) |

## Segment Angle of a Circle Corner formula |
||

\(\large{ \Delta = arccos \; \frac{ 2\;r^2 \;-\; c^2 }{2\;r^2} }\) | ||

Symbol |
English |
Metric |

\(\large{ \Delta }\) = segment angle | \(\large{deg}\) | \(\large{rad}\) |

\(\large{ c }\) = chord length | \(\large{ft}\) | \(\large{m}\) |

\(\large{ r }\) = radius | \(\large{ft}\) | \(\large{m}\) |

Tags: Area Equations Perimeter Equations Arc Length Equations Chord Equations Segment Equations