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Understanding Inscribed Angles and Arc Measures in Circles

This lesson focuses on the concepts of inscribed angles and the relationship between angles and arcs in circles. Students will learn how to find the measure of an inscribed angle and an angle formed by a tangent and a chord. Key topics include the definitions of central angles, major and minor arcs, and how to calculate their measures. Practical examples will be provided to ensure comprehension, followed by a homework assignment to reinforce these concepts.

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Understanding Inscribed Angles and Arc Measures in Circles

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Presentation Transcript

  1. Warm Up • Solve for x

  2. Homework Check • 72 2. 12 3. 10 4. 24 5. 8 6. 10.39 7. 8 8. 105. 116 9. 90 10. 4 11. 9,18,9 12. 110 13. 6

  3. Today’s Objectives • 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.

  4. 11-3 Inscribed Angles • A Central Angle is an angle with vertex at the center of the circle. Central Angle B K C R

  5. Major and Minor Arcs • Minor Arc – Short Distance around Circle • Major Arc – Long Distance around Circle B Minor Arc, BC Major Arc, BRC K C R

  6. Arc Measures • The measure of minor arc = measure of central angle • The measure of major arc = 360 – minor arc mBC = 100* mBRC = 360-100 = 260* B 100° 100° 100° K C R

  7. Inscribed Angles • An Inscribed Angle is an angle with vertex ON the circle • The Measure of an inscribed angle = ½ its arc Inscribed Angle

  8. Example – Find the value of each variable

  9. Example – Find the value of each variable

  10. Example – Find the value of each variable

  11. Example – Find the value of each variable

  12. Example – Find the value of each variable

  13. Example – Find the value of each variable

  14. Example – Find the value of each variable

  15. Homework • Hand out

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