Difference between revisions of "Inradius"
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== Properties == | == Properties == | ||
*If <math>\triangle ABC</math> has inradius <math>r</math> and [[circumradius]] <math>R</math>, then <math>\cos{A}+\cos{B}+\cos{C}=\frac{r+R}{R}</math>. | *If <math>\triangle ABC</math> has inradius <math>r</math> and [[circumradius]] <math>R</math>, then <math>\cos{A}+\cos{B}+\cos{C}=\frac{r+R}{R}</math>. | ||
− | *If <math>\triangle ABC</math> has inradius <math>r</math> and [[semi-perimeter]] <math>s</math>, then the [[area]] of <math>ABC</math> is <math>rs</math>. | + | *If <math>\triangle ABC</math> has inradius <math>r</math> and [[semi-perimeter]] <math>s</math>, then the [[area]] of <math>\triangle ABC</math> is <math>rs</math>. |
[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 13:54, 14 March 2010
The inradius of a polygon is the radius of its incircle (assuming an incircle exists). It is commonly denoted .
Properties
- If has inradius and circumradius , then .
- If has inradius and semi-perimeter , then the area of is .