Difference between revisions of "Circumradius"
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| − | The '''circumradius''' of a triangle 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]]. | + | The '''circumradius''' or any polygon is the radius of the cirumscribed circle of that polygon, if such a circle exists. 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== | ==Formula for a Triangle== | ||
Revision as of 19:04, 8 July 2007
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The circumradius or any polygon is the radius of the cirumscribed circle of that polygon, if such a circle exists. 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 
