# Euler's theorem (triangles)

## Description

The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is called the circumcenter and its radius is called the circumradius.

The incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is called the triangle’s incenter.

Euler’s theorem gives the relation between the circumradius and inradius of a triangle, and the distance between the circumcenter and the incenter.

## Variables

R | Circumradius (m) |

r_{in} | Inradius (m) |

d | Distance between the circumcenter and the incenter (m) |