Investigating Properties of Chords and Arcs
Objective:
Have students understand four theorems concerning properties of chords
and arcs of circles.
Lesson:
Have the students perform some investigations in GSP to help them
deduce some theorems about chords of circles. These theorems are
as follows:
Theorem 1: In a circle, or in two congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. mAOC = mBOC if and only if mAB = mBC 

Theorem 2: If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. If m<ODB = 90o, then mAD = mDB 

Theorem 3: If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. If mAB = mBC then m<OBC = 90^{o} 

Theorem 4: In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center. mDC = mAB if and only if mOE = mOF. 