Explore the relationship between chords of a circle and their perpendicular bisectors.

• You have seen before that for any triangle, you can find a circle that contains all 3 vertices (called the circumscribed circle or the circumcircle). When the 4 vertices of a quadrilateral lie on a circle, it is a special situation and deserves a special name: cyclic quadrilateral. In this activity, students will investigate some of the properties of cyclic quadrilaterals.

• circumscribed circle
• perpendicular bisector
• supplementary angles

This lesson is intended to be introduced by the teacher and completed by the students, as they discover and justify their conjectures. Students might work independently or with a partner to complete this activity. The time varies for this activity depending on whether the TI-Nspire document (.tns file) is given to or created by the students.