A quadrilateral inscribed in a circle has each vertices on the circle (circle is circumcircle).
A quadrilatearl circumscribed to a circle has each side tangent to circle (circle is incircle).
A bicentric quadrilateral combines the two properties : it has both an incircle and a circumcircle.
Construct a bicentric quadrilateral.
Precisely, given three points ABC on a (circum)circle, find D on this circle, such as ABCD has an incircle.