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CENTRAL ANGLE

CENTRAL ANGLE. C. A. B. C. Answer: . A. B. D. C. A. B. By Construction:. Draw a circle with centre C. Draw radii AC and BC. Measure the angle formed. What is the measure of angle ACB? What is the measure of arc AB? Draw chords AD and BC. Measure ADB. What is m.

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CENTRAL ANGLE

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  1. CENTRAL ANGLE C A B

  2. C Answer: A B

  3. D C A B

  4. By Construction: • Draw a circle with centre C. • Draw radii AC and BC. • Measure the angle formed. • What is the measure of angle ACB? • What is the measure of arc AB? • Draw chords AD and BC. • Measure ADB. • What is m

  5. INSCRIBED ANGLE D C A B

  6. An angle whose vertex is on the circle and whose sides are chords of the circle.

  7. INSCRIBED ANGLE THEOREM PROOF The measure of an inscribed angle is half the measure of its intercepted arc.

  8. Cases: • Case 1 • Case 2 • Case 3

  9. Cases: • Case 1 • Case 2 • Case 3

  10. Cases: • Case 1 • Case 2 • Case 3

  11. Cases: EXAMPLE • Case 1 • Case 2 • Case 3

  12. Case 1: B O A PROVED C

  13. Case 2: B O A C PROVED D = = =

  14. Case 3: B O A PROVED C D = =

  15. Example: A In the accompanying figure, mAB=112, mBC=54, and mCD=88. Find m3. B D C SOLUTION

  16. Solution: 112 + 54 + 88 + mDA = 360 mDA = 360 m= mBC EXERCISES mAB + mBC + mCD + mDA = 360 = =27° m2 =mDA = = 53° m3= m1 + m2 = 27 + 53 = 80°

  17. Exercises: D A O B C HOMEWORK In O, AC is a diameter, mAD= 70, and mBDC = 30°. Determine the measures of the following: B C BC AB ADB ADC

  18. Homework: A B D C Given: Quadrilateral ABCD is a rectangle. Prove: AC and BD are diameters of the circle.

  19. C DONE

  20. C A B DONE

  21. D C A B DONE

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