Circumscribed quadrilaterals

A quadrilateral is circumscribed (or tangential) if and only if a circle can be inscribed in it, touching all four sides. This happens if and only if the sums of the lengths of its pairs of opposite sides are equal.

Important properties

• A circle can be inscribed in a quadrilateral if and only if the sums of the lengths of opposite sides are equal: $AB + CD = BC + DA$.

• Each side of the quadrilateral is tangent to the incircle.

• The points where the incircle touches the sides are called points of tangency.