Circumradius: Difference between revisions
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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''' 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]]. | ||
==Formula== | ==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>\frac{abc}{4A}</math> | ||
Revision as of 19:04, 8 July 2007
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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.
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 
