incircle

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

The radius of incircle is given by the formula
 

where A_t = area of the triangle and s = semi-perimeter.
 

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.