# Difference between revisions of "Incircle"

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==Formulas== | ==Formulas== | ||

− | *The radius of an incircle of a triangle (the inradius) with sides <math>a,b,c</math> and area <math> | + | *The radius of an incircle of a triangle (the inradius) with sides <math>a,b,c</math> and area <math>A</math> is <math>\frac{2A}{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>r=\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>r=\frac{ab}{a+b+c}=\frac{a+b-c}{2}</math>. | ||

− | *For any polygon with an incircle, <math> | + | *For any polygon with an incircle, <math>A=sr</math>, where <math>K</math> is the area, <math>s</math> is the semiperimeter, and <math>r</math> is the inradius. |

+ | |||

+ | *The formula for the semiperimeter is <math>s=\frac{a+b+c}{2}</math>. | ||

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+ | *And area of the triangle by Heron is <math>A^2=s(s-a)(s-b)(s-c)</math>. | ||

[[Category:Geometry]] | [[Category:Geometry]] |

## Revision as of 08:33, 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 .