# Difference between revisions of "Incircle"

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

− | *The area of the triangle by [[Heron's Formula]] is <math>A^2=s(s-a)(s-b)(s- | + | *The area of the triangle by [[Heron's Formula]] is <math>A^2=s(s-a)(s-b)(s-c)</math>. |

==See also== | ==See also== |

## Revision as of 07:59, 25 November 2020

*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. For a triangle, the center of the incircle is the Incenter.

## 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 semi perimeter, and is the inradius.
- The coordinates of the incenter (center of incircle) are , if the coordinates of each vertex are , , and , the side opposite of has length , the side opposite of has length , and the side opposite of has length .

- The formula for the semiperimeter is .

- The area of the triangle by Heron's Formula is .

## See also

Click here to learn about the orthrocenter, and Line's Tangent