1. 10.3 - A RCS AND C HORDS Objective: Determine missing parts of a circle using properties of chords and arcs

2. A RC Minor: connects an angle under 180˚ Major: connects an angle over 180˚ C HORD A segment whose endpoints are points on a circle.

3. Butterfly Theorem: Two minor arcs are congruent if and only if their corresponding chords are congruent. AB  CD if and only if AB  CD A B C D

4. Find mCD. 4x° E D C x + 78° B

5. Vitruvian Theorem: If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. DE  EF, DG  GF F G E D O If OG is a diameter of circle O, then

6. Using the Vitruvian Theorem

7. Tug-of-War Theorem: Two chords are congruent if and only if they are equidistant from the center. A F C B AB  CD if and only if EF  EG D G What happens if the segment is also perpendicular?

8. Find CG. E D C B G A F 12 8 Find CE.

9. In Circle R, LM = NO, LM = 6, TR = 4 mLM = 80. 1.) Find mNQ. 2.) Find TO. 3.) Challenge: Find RP.

11. AD = 40 and CD = 25. Find CG. ED C B G A F

12. Find the length of a chord of a circle with radius 8 that is a distance of 5 from the center.

13. AB = 12, DE =12, and CE = 7. Find CG. E D C B G A F

14. Homework: p. 719-720 #12,15-19, 21-23, 38