Name:___________________________________________________
Ch. 9-10 Review worksheet
Period: ____________________
#1-12 Identify an instance of each term in the diagram on the right.
1. center of the circle
7. inscribed angle
2. chord
8. arc
3. secant of the circle
9. major arc
4. tangent of the circle
10. minor arc
5. point of tangency
11. diameter
6. central angle
12. semicircle
Determine the measure of each minor arc.
13.
14.
Determine the measure of each central angle.
15.
16.
Determine the measure of each inscribed angle.
17.
18.
Determine the measure of each intercepted arc.
19.
20.
Use the given information to answer each question.
21. The measure of
is
. What is the
measure of
?
23. In circle C,
. What is
?
22. The measure of
is
measure of
. What is the
?
24. Write an expression for the measure of
∠𝑆𝑆𝑆𝑆𝑆𝑆.
List the intercepted arc(s) for the given angle.
25.
26.
Write an expression for the measure of the given angle.
27.
28.
Use the diagram shown to determine the measure of each angle or arc.
29. Determine
.
30. Determine
31. If the length of
the length of
is 13 millimeters, what is
?
32. If
and
.
, how does the measure of
compare?
33. If
, how does the measure of
and
34. If
and diameter
is
perpendicular to both, what is the relationship
between
and
? Explain your answer.
compare?
Use each diagram and the Segment Chord Theorem to write an equation involving the segments of the
chords.
35.
36.
Calculate the measure of each angle. Explain your reasoning.
37. If
is a tangent segment and
is a
38. If
is a tangent segment and
radius,
what
is the measure of
radius, what is the measure of
?
is a
?
Write a statement to show the congruent segments.
39.
and
are tangent to circle O.
40.
and
are tangent to circle O.
Calculate the measure of each angle. Explain your reasoning.
41. If
and
are tangent segments, what is
42. If
and
are tangent segments, what
the measure of
?
is the measure of
?
Use each diagram and the Secant Segment Theorem to write an equation involving the secant segments.
43.
44.
Name a tangent segment, a secant segment, and an external secant segment for circle O.
45.
46.
Use each diagram and the Secant Tangent Theorem to write an equation involving the secant and tangent
segments.
47.
48.
Draw a triangle inscribed in the circle through the three points. Then determine if the triangle is a right
triangle.
49.
50.
Draw a triangle inscribed in the circle through the given points. Then determine the measure of the
indicated angle.
51. In
. Determine
.
52. In
. Determine
.
Draw a quadrilateral inscribed in the circle through the given four points. Then determine the measure of
the indicated angle.
53. In quadrilateral ABCD,
.
54. In quadrilateral ABCD,
.
Determine
.
Determine
.
Construct a circle inscribed in the polygon.
55.
Calculate the ratio of the length of each arc to the circle’s circumference.
56. The measure of
is
.
57. The measure of
is
.
Write an expression that you can use to calculate the length of
expression.
58.
. You do not need to simplify the
59.
Calculate each arc length. Write your answer in terms of .
60. If the measure of
is
and the diameter is 20 millimeters, what is the arc length of
61. If the measure of
is
and the diameter is 21 centimeters, what is the arc length of
?
?
Calculate each arc length. Write your answer in terms of .
62. If the length of the radius is 11 centimeters,
63. If the length of the radius is 17 centimeters,
what is the arc length of
?
what is the arc length of
?
Use the given information to answer each question. Where necessary, use 3.14 to approximate
64. A circle has a circumference of 81.2 inches. What is the radius of the circle?
.
65. Carla used a string and a tape measure and determine the circumference of a circular cup to be 12.56
inches. What is the radius of the cup?
Solve for each measure given the information.
66. If
and the intercepted arc length is
67. The measure of a central angle is
the formula
, what is the measure of the central angle?
. The length of the radius is 40 mm. Determine the arc length using
.
Calculate the area of each sector. Write your answer in terms of .
68. If the radius of the circle is 24 centimeters,
69. If the radius of the circle is 21 meters, what is
what is the area of sector MON?
the area of sector POQ?
Calculate the area of each segment. Round your answer to the nearest tenth, if necessary. Use 3.14 to
estimate .
70. If the radius of the circle is 25 meters, what is
71. If the radius of the circle is 30 centimeters,
the area of the shaded segment?
what is the area of the shaded segment?
#72-73, In circle O below,
circle O.
. Use the given information to determine the length of the radius of
72. If the area of the segment is
square feet, what is the length of the radius of circle O?
73. If the area of the segment is
square inches, what is the length of the radius of circle O?
74. Draw a picture of an inscribed polygon.
75. Draw a picture of a circumscribed polygon.