Quadrilateral Circumscribing a Circle
Quadrilateral circumscribing a circle (also called tangential quadrilateral) is a quadrangle whose sides are tangent to a circle inside it.
Where r = radius of inscribed circle and s = semi-perimeter = (a + b + c + d)/2
Derivation for area
Let O and r be the center and radius of the inscribed circle, respectively.
Some known properties
- Opposite sides subtend supplementary angles at the center of inscribed circle. From the figure above, ∠AOB + ∠COD = 180° and ∠AOD + ∠BOC = 180°.
- The area can be divided into four kites. See figure below.
- If the opposite angles are equal (A = C and B = D), it is a rhombus.