Difference between revisions of "Incircle"
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*And area of the triangle by Heron is <math>A^2=s(s-a)(s-b)(s-c)</math>. | *And area of the triangle by Heron is <math>A^2=s(s-a)(s-b)(s-c)</math>. | ||
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| + | ==See also== | ||
| + | *[[Circumradius]] | ||
| + | *[[Inradius]] | ||
| + | *[[Kimberling centers]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 08:35, 6 August 2017
This article is a stub. Help us out by expanding it.
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. A quadrilateral that does have an incircle is called a Tangential Quadrilateral.
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 area, 
is the semiperimeter, and 
is the inradius.- The formula for the semiperimeter is
.
.- And area of the triangle by Heron is
.
.
