1. Geometry Basketball Reviewing Circles

2. Find the arc or angle.

3. Solution 55 +65 = 120 180-120=60

4. Find the arc or angle.

5. Solution 55º Vertical Angles are congruent!

6. Find the arc or angle.

7. Solution Semicircle + Arc NB 180 +55 =235

8. Find the arc or angle.

9. Solution Inscribed Angle is ½ of its intercepted arc <ABC = ½(84) =42

10. Find the arc or angle.

11. Solution Inscribed Angle is ½ its intercepted arc <ABC= ½ (arc AC) 65 = ½ (arc AC) 130 = arc AC

12. Find the arc or angle.

13. Solution When the lines intersect ON THE CIRCLE, the angle is ½ of the arc. 135= ½ (MLK) 270 = MLK

14. Find the arc or angle.

15. Solution When the lines intersect ON THE CIRCLE, the angle is ½ of the arc. m<1= ½ (260) m<1 = 130

16. Find the arc or angle.

17. Solution When the lines intersect IN THE CIRCLE, the angle is the sum of the arcs divided by 2. Wrong arcs  125+105=230 360-230=130  Sum of correct arcs m<1=130/2 m<1 = 65

18. Find the arc or angle.

19. Solution When the lines intersect OUTSIDE THE CIRCLE, the angle is the bigger arc –smaller arc divided by 2. m<1= (122-64)/2 m<1 = 58/2 m<1 = 29

20. Find the arc or angle.

21. Solution When the lines intersect OUTSIDE THE CIRCLE, the angle is the bigger arc –smaller arc divided by 2. m<1= (135-55)/2 m<1 = 80/2 m<1 = 40

22. Find the arc or angle.

23. Solution When the lines intersect OUTSIDE THE CIRCLE, Outside segmet (whole segment) = Outside segment (whole segment) 8(x+8) = 9 (9) 8(x+8) = 9² 8x+64=81 8x=17 X=17/8

24. Find the arc or angle.

25. Solution When the lines intersect OUTSIDE THE CIRCLE, Outside segmet (whole segment) = Outside segment (whole segment) 5(3x+5) = 10 (10) 5(3x+5) = 10² 15x+25=100 15x=75 X=5

26. Find the center and radius of the circle.

27. Solution Center : (-3,4) Radius: 6

28. Find the arc or angle.

29. Solution m<KMX = 75 Vertical Angles are Congruent!

30. Find the arc or angle.

31. Solution Semicircle = 180 90 +75 = 165 180 – 165 = 15

32. Find the arc or angle.

33. Solution Semicircle + Arc LY 180 + 75 255

34. Find the arc or angle.

35. Solution Inscribed Angle is ½ its intercepted arc m<TUV= ½ (arc TV) m<TUV = ½ (240) m<TUV = 120

36. Find the arc or angle.

37. Solution When the lines intersect ON THE CIRCLE, the angle is ½ of the arc. 53= ½ (arcAB) 106 = arc AB

38. Find the arc or angle.

39. Solution When the lines intersect IN THE CIRCLE, the angle is the sum of the arcs divided by 2. Use Semicircle  180 – 147 = 33 m<1= (67+33)/2 m<1=100/2 m<1=50

40. Find the arc or angle.

41. Solution When the lines intersect ON THE CIRCLE, the angle is ½ of the arc. Use full circle  360-150=210 m<1= ½ (210) m<1=105

42. Find the arc or angle.

43. Solution When the lines intersect OUTSIDE THE CIRCLE, the angle is the bigger arc –smaller arc divided by 2. Use full Circle  360-234 =126 m<1= (234-126)/2 m<1 = 108/2 m<1 = 54

44. Find x.

45. Solution When the lines intersect IN THE CIRCLE, (part)(part) = (part)(part) (2x)(2x) = (5)(20) 4x²=100 x²=25 x= 5 or -5 (the lengths can’t be negative, so…) x=5

46. Find x.

47. Solution When the lines intersect OUTSIDE THE CIRCLE, (part)(part) = (part)(part) (2x)(2x) = (5)(20) 4x²=100 x²=25 x= 5 or -5 (the lengths can’t be negative, so…) x=5

48. Find x.

50. Find the angle.