inscribe circle
Quadrilateral Circumscribing a Circle
Quadrilateral circumscribing a circle (also called tangential quadrilateral) is a quadrangle whose sides are tangent to a circle inside it.
![Tangential Quadrilateral](/sites/default/files/images/tangential-quadrilateral.gif)
Area,
Where r = radius of inscribed circle and s = semi-perimeter = (a + b + c + d)/2
Derivation for area
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The Regular Polygon
Rhombus is a quadrilateral with all sides equal (equilateral). Rectangle is a quadrilateral with all included angles are equal (equiangular). Square is both equilateral and equiangular, thus square is a regular polygon. Regular polygons are polygons with all sides equal and all included angles equal. Meaning, regular polygons are both equilateral and equiangular.
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Derivation of Formula for Radius of Incircle
The radius of incircle is given by the formula
where At = area of the triangle and s = semi-perimeter.
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Centers of a Triangle
This page will define the following: incenter, circumcenter, orthocenter, centroid, and Euler line.
Incenter
Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection of the angle bisectors of the triangle.
![incenter-incircle.jpg](/sites/default/files/users/Mathalino/plane-geometry/incenter-incircle.jpg)
The radius of incircle is given by the formula
where At = area of the triangle and s = ½ (a + b + c). See the derivation of formula for radius of incircle.
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