12.3 Inscribed Angles

1. 12.3 Inscribed Angles Brett Solberg AHS ‘11-’12

2. Warm-up • 1) What is the measure of arc AC? • 2) What is the arc length of arc AC? • 3) • Get out your notes and HW.

3. HW Review • #8

4. Today’s Agenda • Quiz • 12.3 Inscribed Angles • Last day for retakes

5. Quiz • 3 Problems • 6 minutes • Use your notes • Flip over when done

6. 1) Is BC tangent to circle a? How do you know? • 2) What is the perimeter of the polygon? • 3) Find the value of x.

7. Review • What is the difference between: • arc length • measure of an arc • Measure of an arc = measure of the central angle.

8. Inscribed Circle • Inscribed Angle • Angle whose vertex is on a circle and whose sides are chords. • Intercepted arc • Arc created by an inscribed angle.

9. Example 1 • Identify the inscribed angle and the intercepted arc.

10. Theorem 12.9-Inscribed Angle Theorem • The measure of an inscribed angle is half the measure of its intercepted arc. • ABC = ½AC

11. Demonstration

12. Example 2 • Find the measure of arc AC

13. Example 2 • Find the measure of arc PT and angle R.

14. Example 2 • Find the measure of angle G and angle D.

15. Corollaries to the Inscribed Angle Theorem • 1) Two inscribed angles that share an intercepted arc are congruent. • 2) An angle inscribed by a semicircle is a right angle.

16. Corollaries to the Inscribed Angle Theorem • 3) The opposite angles of a quadrilateral inscribed in a circle are supplementary. • angle N + angle O = 180˚ • angle P + angle M = 180˚

17. Theorem 12.10 • The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

18. Example 4 • RS and TU are diameters of circle A. RB is tangent to circle A at point R. Find the measure of angle BRT and TRS.

19. Assignment • Worksheet 2.3 • EC Assignment Due on THU • pg. 711 #1 – 43 all