Difference between revisions of "Incircle"
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An '''incircle''' of a [[convex]] [[polygon]] is a [[circle]] which is inside the figure and [[tangent line | 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 (geometry) | square]] [[rectangle]]s) do not have an incircle. | An '''incircle''' of a [[convex]] [[polygon]] is a [[circle]] which is inside the figure and [[tangent line | 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 (geometry) | square]] [[rectangle]]s) do not have an incircle. | ||
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| + | ==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 right triangle (the inradius) with legs <math>a,b</math> and hypotenuse <math>c</math> is <math>\frac{ab}{a+b+c}</math> | ||
Revision as of 10:25, 25 October 2007
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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 
and area 
is 
and hypotenuse 
is 
