# hypotenuse

Let $ABC$ a right triangle^{} in a Euclidean geometry^{} with right angle^{} at $C$. Then $AB$ is called the *hypotenuse ^{}* of $ABC$.

The midpoint^{} $P$ of the hypotenuse coincides with the circumcenter^{} of the triangle, so it is equidistant from the three vertices. When the triangle is inscribed^{} on his circumcircle, the hypotenuse becomes a diameter^{}. So the distance^{} from $P$ to the vertices is precisely the circumradius.

The hypotenuse’s length can be calculated by means of the Pythagorean theorem^{}:

$$c=\sqrt{{a}^{2}+{b}^{2}}$$ |

Title | hypotenuse |
---|---|

Canonical name | Hypotenuse |

Date of creation | 2013-03-22 12:02:58 |

Last modified on | 2013-03-22 12:02:58 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 15 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 51-00 |

Synonym | hypothenuse |

Related topic | Triangle |

Related topic | RightTriangle |

Related topic | PythagorasTheorem |

Related topic | Sohcahtoa^{} |