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Central Angle

Central Angle. Vertex OUTSIDE circle. Vertex ON circle. Vertex INSIDE circle. Right Triangles. Time to make a Wheel of Formulas. Cut out this part. Central Angle. Vertex OUTSIDE circle. Vertex ON circle. Vertex INSIDE circle. Right Triangles. Case I: Vertex is ON the circle. ANGLE.

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Central Angle

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  1. Central Angle Vertex OUTSIDE circle Vertex ON circle Vertex INSIDE circle Right Triangles

  2. Time to make a Wheel of Formulas

  3. Cut out this part.

  4. Central Angle Vertex OUTSIDE circle Vertex ON circle Vertex INSIDE circle Right Triangles

  5. Case I:Vertex is ON the circle ANGLE ARC ARC ANGLE

  6. Ex. 1 Find m1. A B 1 124° C m1 = 62°

  7. Ex. 2 Find m1. 1 84° m1 = 42°

  8. Ex. 3 Find the value of x. x = 55°

  9. Ex. 4 Find the mCADif mAB = 60. mCAD= 30°

  10. Case II:Vertex is inside the circle A ARC B ANGLE D ARC C Looks like a PLUS sign!

  11. Ex. 5 Find m1. 93° A B 1 D C 113° m1 = 103°

  12. Ex. 6 Find mQT. mQT = 100° N Q 84° 92° M T

  13. Case III:Vertex is outside the circle C ANGLE small ARC A D LARGE ARC B LARGE ARC LARGE ARC small ARC ANGLE small ARC ANGLE

  14. Ex. 7 Find m1. 1 15° A D 65° B m1 = 25°

  15. Ex. 8 Find mAB. mAB = 16° A 27° 70° B

  16. Ex. 9 Find m1. 260° 1 m1 = 80°

  17. Case IV:Triangle in a semicircle semicircle (180°) semicircle DIAMETER ANGLE ANGLE = 90°

  18. Ex. 10 Find m1. AB is a diameter. m1 = 40° A 1 50° B

  19. Ex. 11 Find m1. AB is a diameter. m1 = 46° A 1 88° C B

  20. Case V:Central Angle ARC ANGLE = ARC ANGLE CENTER

  21. Ex. 12 Find mAB. mAB= 32° C 32° B A

  22. Ex. 13 Find mBC. AC is a diameter. mBC= 148° C 32° B A

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