Difference between revisions of "Incircle"
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*The radius of an incircle of a triangle (the inradius) with sides <math>a,b,c</math> and area <math>K</math> is <math>\frac{2K}{a+b+c}</math> | *The radius of an incircle of a triangle (the inradius) with sides <math>a,b,c</math> and area <math>K</math> is <math>\frac{2K}{a+b+c}</math> | ||
*The radius of an incircle of a right triangle (the inradius) with legs <math>a,b</math> and hypotenuse <math>c</math> is <math>\frac{ab}{a+b+c}=\frac{a+b-c}{2}</math>. | *The radius of an incircle of a right triangle (the inradius) with legs <math>a,b</math> and hypotenuse <math>c</math> is <math>\frac{ab}{a+b+c}=\frac{a+b-c}{2}</math>. | ||
| + | *For any polygon with an incircle, <math>K=sr</math>, where <math>K</math> is the area, <math>s</math> is the semiperimeter, and <math>r</math> is the inradius. | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 14:06, 1 January 2014
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An incircle of a convex polygon is a circle which is inside the figure and tangent to each side. Every triangle and regular polygon has a unique incircle, but in general polygons with 4 or more sides (such as non- square rectangles) do not have an incircle.
Formulas
- The radius of an incircle of a triangle (the inradius) with sides
and area 
is 
- The radius of an incircle of a right triangle (the inradius) with legs
and hypotenuse 
is 
. - For any polygon with an incircle,
, where is the area, 
is the semiperimeter, and 
is the inradius.
and area 
is 
and hypotenuse 
is 
.
, where 
is the semiperimeter, and 
is the inradius.
