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Warm-up

Warm-up . A. 1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle. N. M. 50. C. P. 3. MCY = 270 Find BC. B. 2. Find ACB. 20. B. A. M. 312. 20. 90. B. 24. C. C. Y. The Circle. ( page 67) MM2G3 Students will understand the properties of circles .

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Warm-up

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  1. Warm-up A 1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle. N M 50 C P 3. MCY = 270 Find BC. B 2. Find ACB 20 B A M 312 20 90 B 24 C C Y

  2. The Circle • (page 67) MM2G3 Students will understand the properties of circles. • (page 69) MM2G3bUnderstand and use properties of central, inscribed, and related angles .

  3. Central Angle Vertex OUTSIDE circle Vertex ON circle Vertex INSIDE circle

  4. Secant AnglesandSecant – Tangent Angles

  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 = 62º

  7. Ex. 2 Find m1. 1 84° m1 = 42º

  8. 108° Ex. 3 Find m1. 1 252° m1 = 126º

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

  10. Ex. 4 Find m1. 93° A B 1 D C 113° m1 = 103º

  11. Ex. 5 Find mQT. mQT = 100º N Q 84º 92º M T

  12. Case IIa: Vertex is inside the circle at the circle’s center Central angle = ARC

  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. 6 Find m1. 1 15° A D 65° B m1 = 25º

  15. Ex. 7 Find mAB. mAB = 16º A 27° 70° B

  16. Ex. 8 Find m1. 260° 1 100° m1 = 80º

  17. 52.5º 4 32º 2 Brain Buster 3 105º 36.5º 1 105º 16º

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