1. 8-2C Radius-chord Conjectures What is a chord? What special relationship exists between a radius of a circle and a chord?

2. Definition A chord is a line segment that joins two points on a circle. AB is a chord of סּD Where would you find the largest chord in any circle? A B D

3. Striking a Chord 1.Draw two chords on your circle that do not contain the center. 2.Can you predict if and where the perpendicular bisectors of the chords will meet? 3.Fold your circle to construct the perpendicular bisector of each chord. 4.Add a third chord. Predict where the perpendicular bisector will meet the other perpendicular bisectors. 5.Fold your circle to construct the 3 rd perpendicular bisector.

4. Find the distance from chord PQ to the center of סּO The radius of circle O is 13 mm. Draw a radius connecting it to one end of the chord. Draw the perpendicular bisector from the center to the chord. How long is PR? What theorem do you use to find the distance from the chord to the center of the circle? OR 2 + 5 2 = 13 2 OR = 12 mm O PQ 10 mm 13 mm R

5. Propose a conclusion X D CA B

6. Y H E F G

7. m contains Z Z K J m

8. Theorem The perpendicular bisector of a chord contains the center of the circle.

9. Theorems If a radius of a circle bisects a chord of the circle that is not a diameter, then it is perpendicular to the chord. If a radius of a circle is perpendicular to a chord of the circle, then it bisects the chord.

10. Theorem In a circle (or in congruent circles), minor arcs are congruent if and only if they have congruent chords.

11. What is a chord? A chord is a line segment that joins two points on a circle. What special relationship exists between a radius of a circle and a chord? If a radius of a circle bisects a chord of the circle that is not a diameter, then it is perpendicular to the chord.

12. Assignment 8-2C Page 577, 1-7, 12-15, 20-22