# Difference between revisions of "Circumradius"

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==Formula for a Triangle== | ==Formula for a Triangle== | ||

− | Let <math>a, b</math> and <math>c</math> denote the triangle's three sides, and let <math>A</math> denote the area of the triangle. Then, the measure of the of the circumradius of the triangle is simply <math>\frac{abc}{4A}</math> | + | Let <math>a, b</math> and <math>c</math> denote the triangle's three sides, and let <math>A</math> denote the area of the triangle. Then, the measure of the of the circumradius of the triangle is simply <math>R=\frac{abc}{4A}</math> |

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+ | Also, <math>A=\frac{abc}{4R}</math> | ||

==Euler's Theorem for a Triangle== | ==Euler's Theorem for a Triangle== |

## Revision as of 22:38, 17 October 2011

*This article is a stub. Help us out by expanding it.*

The **circumradius** of a cyclic polygon is the radius of the cirumscribed circle of that polygon. For a triangle, it is the measure of the radius of the circle that circumscribes the triangle. Since every triangle is cyclic, every triangle has a circumscribed circle, or a circumcircle.

## Formula for a Triangle

Let and denote the triangle's three sides, and let denote the area of the triangle. Then, the measure of the of the circumradius of the triangle is simply

Also,

## Euler's Theorem for a Triangle

Let have circumradius and inradius . Let be the distance between the circumcenter and the incenter. Then we have