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

• Students will explore the relationship between chords of a circle and their perpendicular bisectors.
• Students will discover that the perpendicular bisector of a chord always passes through the center of a circle.
• Students will discover that a line perpendicular to a chord that passes through the center of a circle always bisects the chord. Students then apply these relationships to right triangles.
• Students will discover that two chords are congruent if and only if they are equidistant from the center of a circle.

• chord of a circle
• perpendicular bisector
• equidistant

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.