1. 10.2– Find Arc Measures

2. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C

3. TermDefinitionPicture Minor Arc Arc of a circle that is less than 180° P A C Two letters:

4. TermDefinitionPicture Major Arc Arc of a circle that is more than 180° P A C 3 letters: B

5. TermDefinitionPicture Semicircle Arc of a circle that is 180° P A C 3 letters: B

6. TermDefinitionPicture Congruent circles Two circles with the same radius

7. TermDefinitionPicture Congruent arcs Arcs that have the same central angle A B C D

8. The measure of a minor arc is the measure of its _____________ angle. central P A C x°x° x°x°

9. 73° minor

10. 73° 107° 26° minor

11. 73° 154° 26° minor

12. 73° 206° 26° 107° major

13. 73° 81° 26° 107° minor

14. 73° 180° 26° 107° semicircle

15. 73° 180° 26° 107° Semicircle

16. 73° 287° 26° 107° major

17. 10.4 – Use Inscribed Angles and Polygons

18. An angle whose vertex is on a circle and whose sides are chords of the circle Inscribed angle:

19. An arc that is inside an inscribed angle Intercepted Arc:

20. A polygon that has all of its vertices on a circle Inscribed Polygon :

21. The circle that contains the vertices of a polygon Circumscribed Circle:

22. The measures of an inscribed angle is ________ the measure of its ______________ arc. half intercepted  D = AB 2 x°x° 2x°

23. If two inscribed angles of a circle _____________ the same arc, then the angles are _____________. intercept congruent D  CD  C

24. A ________ triangle is inscribed in a circle iff the _______________ is a diameter of the circle. right hypotenuse  B is a right angle because it inscribes a semicircle.

25. A ____________________ can be inscribed in a circle iff its opposite angles are ______________. quadrilateral supplementary m  D + m  F = 180° m  E + m  G = 180°

26. Find the indicated measure. = 158 2 = 79°

27. Find the indicated measure. = 180 2 = 90° 180° 90°

28. Find the indicated measure. = 40  2 = 80°

29. Find the indicated measure. = 88° 92° 92 2 = 46°

30. Find the indicated measure. = 80 2 = 40° 100° 80°

31. Find the indicated measure. = 56 2 = 28° 56°

32. Find the measure of  A and  C. 80° m  A = 80 2 = 40° 64° m  C = 64 2 = 32°

33. Find the measure of  A and  C. m  A = 146 2 = 73° m  C = 62 2 = 31° 146° 62°

34. m  PNO = 68 2 = 34°

35. m  QNP = 62 2 = 31° 62°

36. =

37. =130° 62°

38. =112° 62° 112°

39. =248° 62° 112°

40. Decide whether a circle can be circumscribed about the figure. 70 + 130  180 No,

41. Decide whether a circle can be circumscribed about the figure. 91 + 89 = 180 Yes, 91°

42. Decide whether a circle can be circumscribed about the figure. 115 + 63  180 No,

43. Find the value of the variables. 5x + 110 = 180 5x = 70 x = 14° 2y + 104 = 180 2y = 76 y = 38°

44. Find the value of the variables. x + 108 = 180 x = 72° y + y = 180 2y = 180 y = 90°

45. Find the value of the variables. 4x = 84+44 2 8x = 128 x = 16° 7y = 152+44 2 14y = 196 y = 14° 44° 11

46. Find the value of the variables. 12x = 96+48 2 24x = 144 x = 6° 3y = 48+171 2 6y = 219 y = 36.5° 171° 11

47. 10.2 10.4 662-663 676-679 3-12, 16, 17, 22, 23 3-8, 11-15 odd, 16, 18 HW Problem 10.4 #15 3a = 54+66 2 6a = 120 a = 20° 4b = 66+110 2 8b = 176 b = 22° 66° 11