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-c)</math>. |
==See also== | ==See also== | ||
Revision as of 23:49, 17 July 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 .
and area 
is 
and hypotenuse 
is 
.
, where 
is the semi perimeter, and 
is the inradius.
, if the coordinates of each vertex are 
, 
, and 
, the side opposite of 
, 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
