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