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Warm Up

Warm Up. Solve for x. 10 minutes. End. Today’s Objectives. 11-3 Inscribed Angles Students will be able to find the measure of an inscribed angle. Students will be able to find the measure of an angle formed by a tangent and a chord. Central Angle.

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Warm Up

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  1. Warm Up • Solve for x 10 minutes End

  2. Today’s Objectives 11-3 Inscribed Angles • Students will be able to find the measure of an inscribed angle. • Students will be able to find the measure of an angle formed by a tangent and a chord.

  3. Central Angle • Definition: A Central Angle is an angle whose vertex is at the center of the circle. Central Angle B K C

  4. Major and Minor Arcs • Minor Arc – Short Distance around Circle • Major Arc – Long Distance around Circle B Minor Arc, BC Major Arc, BRC K Use three points to name a major arc C R

  5. Arc Measures • Measure of a minor arc = Measure of central angle • Measure of major arc = 360o– Measure of Minor Arc • Why? mBC = 100o mBRC = 360o - 100o= 260o B 100° 100° 100° K C R

  6. Inscribed Angles • Definition: An Inscribed Angle is an angle whose vertex is ON the circle Inscribed Angle ∠JKL J 100° “Intercepted Arc” JL L K

  7. Theorem 6 • Measure of an Inscribed Angle = ½ its intercepted arc m∠JKL = ½(mJL) = ½(30°) = 15° J 30° 100° L K

  8. Corollary 1 • Opposite angles of a quadrilateral inscribed in a circle are supplementary • Why?

  9. Other Corollaries to think about • Corollary 2: Two inscribed angles that intercept the same arc are congruent • Corollary 3: An angle inscribed in a semicircle is a right angle.

  10. Theorem 7 • The measure of an angle formed by a tangent line and a chord is half the measure of the intercepted arc. R Chord Intercepted Arc 100° S Angle m∠RTU = ½ mRST U T Tangent Line

  11. Example – ON PAGE 5 Find the values of a, b, and c

  12. Example – Find the values of x and y

  13. Example – Find the values of w and u

  14. Example – Find the values of a, b, c, and d

  15. Example – Find the value of each variable

  16. Example – Find the value of each variable

  17. Example – Find the value of each variable

  18. Classwork • Arrange desks in groups • As a group, complete page 6of Unit 8 packet • Be prepared to have your work displayed on doc cam!

  19. Homework Assignment • Finish page 6 of packet • Study for QUIZ tomorrow

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