1. Brain Trainer  Find the following measures. 1) Arc RJ 2) m<JSL 3) Arc JL 4) Name a major arc. 5) Name a minor arc. 6) Name a semicircle. S R J L 170 0 E

2. Arcs and Chords Lesson 10.3 Indiana Standard G.6.2

3. Arcs and Chords The endpoints of a chord are also endpoints of an arc. Arc AB starts at point A and ends at point B. AB

4. Arcs and Chords  In a circle or in congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent. If chords AB and CD are congruent, then arcs AB and CD are congruent. A B C D

5. Example Assume AB and XY are congruent. ABXY A B X Y 10 25 10 25

6. Inscribed Polygons  The chords of adjacent arcs can form a polygon. A polygon is inscribed if all of its vertices lie on the circle. Circle A is CIRCUMSCRIBED about the polygon because it contains all the vertices of the polygon.. A Q R S T U

7. Diameters and Chords  In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. If BA TV, then UT = UV and AT = AV. C U B A VT ~~

8. Examples  CD = 24, radius = 13 mCD = 134, find mCB Find DS Find PS (Hint: use pythagorean theorem) 12 2 + (x) 2 = 13 2 (x) 2 = 25 PX = 5. 13 C D B P S 67 12 x

9. Homework Marker Board!

10. Last example  AB = 20, radius = 15 Find EF FB = 10 10 2 + x 2 = 15 2 x 2 = 125 EF = 11.18 A B C D. E F 15 10 x

11. Problem 1  Solve for x. A B C D 2x - 12 36 24

12. Problem 2 A B C D 14 (x + 17) 0 Solve for x. (4x + 2) 0 5

13. Problem 3 AB = 12, radius = 8 mAB = 72, find mCB Find AF Find EF (Hint: use pythagorean theorem) A B C D. E F 8 6 5.3 x

14. Problem 4 AB = 26, radius = 20 mAB = 24, find mAC Find BF Find EF (Hint: use pythagorean theorem) A B C D. E F 13 20 15.2 x

15. Problem 5 CD = 32, radius = 22 mCD = 100, find mCB Find DL Find PL (Hint: use pythagorean theorem) 16. C D B P L 22 15.1 x

16. Problem 6 CD = 42, radius = 25 mCD = 24, find mBD Find CA Find PA (Hint: use pythagorean theorem) 21. C D B P A 25 13.6 x