Circumradius

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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,

Formula for Circumradius

Where is the Circumradius, is the inradius, and , , and are the respective sides of the triangle. Note that this is similar to the previously mentioned formula; the reason being that .

Euler's Theorem for a Triangle

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

See also

• Inradius
• Semiperimeter