# 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 07:35, 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.

- The formula for the semiperimeter is .

- And area of the triangle by Heron is .