Name_____________________________________________
Unit 5 Circles – Review Packet
1. Line ⃡𝐵𝐹 intersects circle E only at point F, and ⃡𝐴𝐶
intersects circle E at points D and F. Which line segment
is tangent to circle E?
Tangent touches a circle at only one point.
2. Line ⃡𝐵𝐹 intersects circle E only at point F, and ⃡𝐴𝐶 intersects
circle E at points D and F. Which line segment is a secant of
circle E?
Secant touches a circle at two points and passes through the circle
3. Line ⃡𝐵𝐹 intersects circle E only at point F, and ⃡𝐴𝐶 intersects
circle E at points D and F. Which line segment is a chord of
circle E?
A chord touches a circle at two points and does not extend beyond
the circle
4. Draw a circle with diameter 𝑃𝑄.
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Name_____________________________________________
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5. Move Q to a different spot on the outside of the circle, leaving P where it was originally.
6. Is 𝑃𝑄 still the diameter? If not, what is it now?
7. In circle O, 𝐾𝑁 is a diameter and the m⦟MON = 60. If the
m⦟LKN = 40, what is the measure of Arc LM?
Arc LM is a portion of Arc LMN. We can find Arc LMN from
inscribed angle LKN. Arc LMN – Arc MN will give us our answer.
8. In circle O, 𝐾𝑁 is a diameter and the m⦟MON = 50. If the
m⦟LKN = 60, what is the measure of Arc LM?
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9. In circle O, 𝐾𝑁 is a diameter and the m⦟MON = 45. If the
m⦟LKN = 50, what is the measure of Arc LM?
10. In the circle, if the m⦟ABC = 30, what is the measure of
⦟ADC?
Angle ADC is an inscribed angle. It is half the measure of the arc.
11. If the m⦟ABC = 50, what is the measure of ⦟ADC?
12. If the m⦟ABC = 45, what is the measure of ⦟ADC?
13. What is the m⦟CAO?
14. What is the m⦟OAB?
15. What is the m⦟BCA?
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Name_____________________________________________
16. What is the measure of angle ABC?
17. What is the measure of angle ACB?
18. What is the measure of angle BAC?
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Name_____________________________________________
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19. What is the measure of Arc MLO?
20. What is the measure of Arc MNO?
L
21. What is the measure of angle MPO?
120o
22. What is the measure of angle BCD?
110o
90o
23. What is the measure of angle BCD?
110o
120o
80o
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24. What is the measure of angle BCD?
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100o
120o
100o
25. A regular hexagon, with sides measuring 8 units, is
inscribed in a circle. What is the area, in square units, of
the circle?
A hexagon is made up of equilateral triangles
26. A regular hexagon, with sides measuring 6 units, is
inscribed in a circle. What is the area, in square units, of
the circle?
27. A regular hexagon, with sides measuring 9 units, is inscribed
in a circle. What is the area, in square units, of the circle?
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28. In circle O, CB is a diameter. What is the measure of
angle ABC?
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100o
An inscribed triangle with diameter as side is a right triangle.
29. In circle O, CB is a diameter. What is the measure of
angle ABC?
120o
30. In circle O, CB is a diameter. What is the measure of
angle ABC?
90o
31. In the following diagram, quadrilateral ABCD is
inscribed in a circle. What is the measure of
angle C?
Inscribed quadrilateral has opposite angles
supplementary.
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32. In the following diagram, quadrilateral ABCD
is inscribed in a circle. What is the measure
of angle D?
33. In the following diagram, quadrilateral ABCD is
inscribed in a circle. What is the measure of
angle C?
34. Dana wants to decorate the wheel of a
bike by weaving a ribbon between the
spokes. The radius at the inside edge of
the tire is 10 in. Dana will weave the
ribbon 1 inch from the inside edge of the
tire, as shown in the figure. The amount of
ribbon used to weave between the spokes
is negligible. Assume the ribbon forms a
circular shape. What is the length of the
ribbon, to the nearest tenth of an inch,
needed to decorate the wheel?
98
Name_____________________________________________
Date________________
35. Dana wants to decorate the wheel of a
bike by weaving a ribbon between the
spokes. The radius at the inside edge of
the tire is 9 in. Dana will weave the ribbon
1 inch from the inside edge of the tire, as
shown in the figure. The amount of ribbon
used to weave between the spokes is
negligible. Assume the ribbon forms a
circular shape. What is the length of the
ribbon, to the nearest tenth of an inch,
needed to decorate the wheel?
36. Dana wants to decorate the wheel of a
bike by weaving a ribbon between the
spokes. The radius at the inside edge of
the tire is 8 in. Dana will weave the ribbon
1 inch from the inside edge of the tire, as
shown in the figure. The amount of ribbon
used to weave between the spokes is
negligible. Assume the ribbon forms a
circular shape. What is the length of the
ribbon, to the nearest tenth of an inch,
needed to decorate the wheel?
37. A Ferris wheel with 20 equally spaced seats has a diameter of 30 m. What is the length, in
meters, between consecutive seats?
38. A Ferris wheel with 20 equally spaced seats has a diameter of 28 m. What is the length, in
meters, between consecutive seats?
Name_____________________________________________
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39. A Ferris wheel with 20 equally spaced seats has a diameter of 32 m. What is the length, in
meters, between consecutive seats?
40. Circle O has a radius of 10 cm. What is the length, in
centimeters, of Arc AB?
41. Circle O has a radius of 10 cm. What is the length, in
centimeters, of Arc AB?
42. Circle O has a radius of 10 cm. What is the length, in
centimeters, of Arc AB?
43. A large pizza has a 15-inch diameter and a medium pizza has a 12-inch diameter. To the nearest
hundredth, how many more square inches of pizza does a customer get with a large than with a
medium?
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Date________________
44. A large pizza has a 16-inch diameter and a medium pizza has a 12-inch diameter. To the nearest
hundredth, how many more square inches of pizza does a customer get with a large than with a
medium?
45. A large pizza has a 16-inch diameter and a medium pizza has a 14-inch diameter. To the nearest
hundredth, how many more square inches of pizza does a customer get with a large than with a
medium?
46. In this figure, the vertices of square ABCD lie on circle O. The area of
ABCD is 100 in2. What is the approximate area of circle O, in square
inches?
47. In this figure, the vertices of square ABCD lie on circle O. The area of
ABCD is 100 in2. What is the approximate area of circle O, in square
inches?
48. In this figure, the vertices of square ABCD lie on circle O. The area of
ABCD is 100 in2. What is the approximate area of circle O, in square
inches?
Name_____________________________________________
Date________________
49. Danielle has 40 yd of fencing to enclose a safe space for her pet rabbits. She has narrowed
down her choices to either a square or a circular enclosure. Which one would provide more
area for her rabbits, and by how many square yards, to the nearest 0.1 yd2?
50. Danielle has 20 yd of fencing to enclose a safe space for her pet rabbits. She has narrowed
down her choices to either a square or a circular enclosure. Which one would provide more
area for her rabbits, and by how many square yards, to the nearest 0.1 yd2?
51. Danielle has 30 yd of fencing to enclose a safe space for her pet rabbits. She has narrowed
down her choices to either a square or a circular enclosure. Which one would provide more
area for her rabbits, and by how many square yards, to the nearest 0.1 yd2?
52. What is the center of the circle with equation (𝑥 − 2)2 + (𝑦 + 3)2 = 25?
53. What is the center of the circle with equation (𝑥 − 3)2 + (𝑦 + 4)2 = 25?
54. What is the center of the circle with equation (𝑥 − 5)2 + (𝑦 + 2)2 = 25?
Name_____________________________________________
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55. A circle has center (3, -4) and a radius of 2√5. What is the equation?
56. A circle has center (2, -5) and a radius of 3√5. What is the equation?
57. A circle has center (3, -5) and a radius of 2√3. What is the equation?
58. What is the equation of the circle centered at (-1,5) and passing through the origin?
59. What is the equation of the circle centered at (-2,5) and passing through the origin?
60. What is the equation of the circle centered at (-1,4) and passing through the origin?