Constructing a general Bicentric Quadrilateral

Bicentric quadrilaterals are quadrilaterals that have their vertices inscribed on a circle (cyclic) as well as their sides circumscribed around (tangential to) a circle. They therefore have an incircle as well as a circumcircle, and have many interesting geometric properties that can be explored with dynamic geometry. An example of a general bicentric quadrilateral is shown below.

Bicentric Quadrilateral

Challenge: A simple example of a bicentric quadrilateral is a square. But can you find a method to accurately construct a (general) bicentric quadrilateral by hand or by using dynamic geometry software? If so, can you find other methods?

Only if stuck, go to some possible constructions.


Back to "Dynamic Geometry Sketches"

Back to "Student Explorations"

Created 25 May 2021 by Michael de Villiers.