Difference between revisions of "Inradius"
m |
(→Properties) |
||
| Line 3: | Line 3: | ||
== 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>. | |
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 14:03, 4 January 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 
.
has inradius 
, then 
.
, then the 
is 
.
