Art of Problem Solving

Circumradius: Difference between revisions

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* [[Inradius]]
* [[Inradius]]
* [[Semiperimeter]]
* [[Semiperimeter]]
[[Category:Geometry]]

Revision as of 09:33, 6 November 2007

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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 $a, b$ and $c$ denote the triangle's three sides, and let $A$ denote the area of the triangle. Then, the measure of the of the circumradius of the triangle is simply $\frac{abc}{4A}$

See also