# Relation between the sides, the dinstances of the orthocenter from the vertices and the circumradius of a triangle

## Description

Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude. The intersection between the extended base and the altitude is called the foot of the altitude. The length of the altitude, often simply called the altitude, is the distance between the extended base and the vertex. The three altitudes intersect in a single point, called the orthocenter of the triangle. Denote the orthocenter of triangle ABC as H, denote the sidelengths as a, b, and c, and denote the circumradius of the triangle as R and then there is a relation between them.

Related formulas## Variables

a | Side of the triangle (opposite of the angle A) (m) |

b | Side of the triangle (opposite of the angle B) (m) |

c | Side of the triangle (opposite of the angle C) (m) |

AH | Distance of the orthocenter from the vertex A (m) |

BH | Distance of the orthocenter from the vertex B (m) |

CH | Distance of the orthocenter from the vertex C (m) |

R | The circumradius of the triangle (m) |