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.
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.
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Created 25 May 2021 by Michael de Villiers.