Difference between revisions of "Incircle"
(→Formulas) |
(→Formulas) |
||
Line 12: | Line 12: | ||
*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>. | ||
+ | |||
+ | |||
+ | ==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.
- The formula for the semiperimeter is
.
- And area of the triangle by Heron is
.