1. Review Ch. 10 Complete all problems on a separate sheet of paper.
Be sure to number each problem. Good Luck!

2. Find the exact length of arc AB, if circle
Problem #1
Find the exact length of arc AB, if circle
P has a radius of 18cm. A P
100° B

3. Solution to #1
Arc Length = (100/360) * 36π = (5/18) * 36π = 10π cm.

4. Problem # 2
Find the diameter of a circle in which a 36 cm chord is 80 cm from the center.

5. Solution to #2
This is a 9, 40, 41 triangle times 2 so r = 82cm  diameter = 164 cm.

6. Find the radius of a circle with a circumference of
Problem #3
Find the radius of a circle with a circumference of

7. Solution to #3
Circumference = π * diameter  so the diameter must be 20  so radius = 10.

8. Find the measure of arc AE.
Problem #4
Find the measure of arc AE. A
200о B x
210о D E C

9. Solution to #4
*Arc BC = 360 – 210 = 150о *Angle BDC is supp (tangent-tangent) = 30о *So Angle ADE = 30о *So 30 = (1/2)(200 – x) 60 = 200 – x x = 140о

10. In the circumscribed polygon, find the length of the AB.
Problem #5
In the circumscribed polygon, find the length of the AB. 15 A 10 B 12

11. Solution to #5
AB = 15 – (10 – x) + 12 – x = 5 + x + 12 – x = 17

12. In circle O, AB is a diameter.
Problem #6
In circle O, AB is a diameter.
OA=3x+5 and OB=2(5x-1).
Find AB.

13. Solution to #6
OA and OB are both radii so are equal. 3x + 5 = 2(5x – 1) 3x + 5 = 10x – 2 7 = 7x 1 = x each radius = 8 ; so diameter AB = 16

14. Problem #7
Solve for x if
and if A B C

15. Solution to #7
Since angle A is inscribed; 2(5x + 6) = 12x – 2 10x + 12 = 12x – 2 14 = 2x x = 7

16. Problem #8 MATH is inscribed in the circle.
Angle M has a measure of 78 degrees.
Find the measure of angle T. A M T H

17. Solution to #8
Opp. Angles of inscribed quadrilaterals are supp. Measure of Angle T = 180 – 78 = 102о

18. Find the radius of the circle if AB is a diameter, , and BC=20.
Problem #9
Find the radius of the circle if AB is a diameter, , and BC=20. A B C

19. Solution to #9
*Measure of Angle B = 120/2 = 60 *Measure of Angle C = 90 *30 – 60 – 90 triangle with x = 20 ; so diameter is 2x = 40 *Radius of AB is 20.

20. A circle is inscribed in triangle ABC. AB=14, AC=12 and BC=4. Find BD.
Problem #10
A circle is inscribed in triangle ABC. AB=14, AC=12 and BC=4. Find BD. A B C D

21. Solution to #10
14 – x + 12 – x = 4 26 – 2x = 4 22 = 2x x = 11 So BD = 14 – x = 3

22. Problem #11
A circle has a radius of 50. How far from the center is a chord of length 28?

23. Solution to #11
7, 24, 25 right triangle So x = 2 * 24 = 48

24. A regular octagon is inscribed in a circle.
Problem #12
A regular octagon is inscribed in a circle.
What is the measure of an arc cut off by a side of the octagon?

25. Solution to #12
* Regular - so all chords congruent. * Congruent chords = congruent arcs. 360/8 = 45о

26. Problem #13
Two concentric circles have radii of lengths 16 and 20. Find the length of a chord of the larger circle that is tangent to the smaller circle.

27. Solution to #13 3, 4, 5 right triangle x = 12 so length of the chord
is 24.

28. A 12 by 10 rectangle is inscribed in a circle. Find the radius.
Problem #14
A 12 by 10 rectangle is inscribed in a circle. Find the radius.

29. Solution to #14
= c2
244 = c2

30. Problem #15
Two secants drawn to a circle from an external point intercept arcs that are 122° and 68°. Find the measure of the secant-secant angle.
122°
68° P

31. Solution to #15
Angle P = (1/2)(122 – 68)
= (1/2)(54)
= 27о

32. Problem #16
Find the circumference of a circle in which an 80 cm chord is 9 cm from the center.

33. Solution to #16 9, 40, 41 right triangle so r = 41 C = 2π(41)
= 82 π cm

34. Problem #17
A central angle intercepts an arc that is 5/12 of the circle. Find the measure of angle x. O x
of circle O

35. Solution to #17
If arc is 5/12  central angle is 5/12 of 360 so central angle is 150о
Radii are congruent so isosceles triangle  only 30о left.
Angle x = 30/2 = 15о

36. If PA and PB are tangent to circle O at A
Problem #18
If PA and PB are tangent to circle O at A
and B, PA=24, and PO=26, find
perimeter of quadrilateral PAOB. A O P B

37. Solution to #18 OA is perpendicular to PA  5, 12, 13 right triangle.
OA = 10 and PB = 24
= 68

38. Find the measure of angle x.
Problem #19
Find the measure of angle x. x
44°
92°

39. Solution to #19

40. Problem #20
What is the length of a chord that cuts off an arc of 120 degrees in a circle with a radius of 8?

41. Solution to #20

42. Problem #21
Parallelogram ABCD is inscribed in circle Q, with dimensions of 24 by 10. Find the area of circle Q.

43. Solution to #21

44. Problem #22
Circle A has a radius of 5 inches, and circle B has a radius of 20 inches. The centers are 39 inches apart. Find the length of the common external tangent (CD). D C • • • A • B

45. Solution to #22

46. Problem #23
Two tangent segments of a circle with a diameter of 50 inches form a 60 degree angle where they meet at P. How far is P from the center of the circle? P
60°

47. Solution to #23

48. Problem #24 AB & AC are tangent to the circle.
Find the measure of arc BDC. A B C D
76°

49. Solution to #24

50. STUDY!!!!!