Tangential quadrilateral

A tangent quadrilateral is a quadrilateral whose sides are tangents of a circle. This circle is called the inscribed circle of the tangent quadrilateral.

The (green shown here ) perpendicular from the incenter (M) on the four sides decompose the tangent quadrilateral in four dragons squares ( with gray subscribed symmetry axes).

A tangent square the sum of two opposing sides (eg, and ) equal to the sum of the other two sides (and). It is therefore

Conversely, also, that every convex quadrilateral with this property () has an inscribed circle and thus a tangent quadrilateral is ( set of pitot ).

The midpoint M of the inscribed circle is located at the intersection of the bisector (shown in gray ) of all four corner brackets (ABCD ). Therefore, all bisectors must intersect in one point, the tangent quadrilateral.

An interesting special case is when a tangent quadrilateral the condition

Met. Under this assumption, the tangent square is also a cyclic quadrilateral, ie a square with radius; this of course does not agree with the inscribed circle. The formula for surface tendons squares provides in this case the simple result

Special tangent squares are the diamond, the square and the kite quadrilateral.