# incircle

## Quadrilateral Circumscribing a Circle

Quadrilateral circumscribing a circle (also called tangential quadrilateral) is a quadrangle whose sides are tangent to a circle inside it.

Area,

Where r = radius of inscribed circle and s = semi-perimeter = (a + b + c + d)/2

**Derivation for area**

## Derivation of Formula for Radius of Incircle

The radius of incircle is given by the formula

where A_{t} = area of the triangle and s = semi-perimeter.

## 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.

The radius of incircle is given by the formula

where A_{t} = area of the triangle and s = ½ (a + b + c). See the derivation of formula for radius of incircle.