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>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>.
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*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>K=sr</math>, where <math>K</math> is the area, <math>s</math> is the semiperimeter, and <math>r</math> is the inradius.
 
*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 08:31, 6 August 2017

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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. 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 $a,b,c$ and area $K$ is $\frac{2K}{a+b+c}$
  • The radius of an incircle of a right triangle (the inradius) with legs $a,b$ and hypotenuse $c$ is $r=\frac{ab}{a+b+c}=\frac{a+b-c}{2}$.
  • For any polygon with an incircle, $K=sr$, where $K$ is the area, $s$ is the semiperimeter, and $r$ is the inradius.
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