In the assignment Inscribing and Circumscribing Triangles, we saw how to circumscribe a triangle with a circle. We also saw that you could circumscribe any triangle. In this assignment we determine if and when you can circumscribe a quadrilateral.
One thing we learned will help us with this. We saw in the assignment Drawing Circles Through Points that three points determine a circle. In other words, if you have three points, then there is only one circle containing the three points.
Any rectangle can be circumscribed, as you will see. However, not all quadrilaterals can be circumscribed. Recalling how one circumscribes a triangle and a rectangle, and recalling that three points determine a circle, find a procedure that will give you a circle passing through the four vertices of a quadrilateral, provided that the quadrilateral can be circumscribed. Test your procedure with the quadrilaterals drawn below.
Problem 1. Describe a procedure that will circumscribe a quadrilateral, provided that there is a circle that circumscribes the quadrilateral. Also, state how your procedure determines when no such circle exists.
Problem 2. Suppose that you are going to explain to a class how to circumscribe a quadrilateral (when it is possible). You want to draw two or three quadrilaterals that can be circumscribed. How can you draw quadrilaterals that are not rectangles that can be circumscribed? Describe a method for producing such quadrilaterals. (Note: you are not being asked to find a general condition for when a quadrilateral can be circumscribed.)
The four quadrilaterals below are examples on which to test your procedure. Of the four, at least one can be circumscribed and at least one cannot be circumscribed.
This document is intended to be printed so that each quadrilateral prints on a separate page.
