AnswersMath II CR S2 RS3Equation of a Circle

Equation of a Circle — Unit test Answers

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1
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Consider circle Y with radius 3 m and central angle XYZ measuring 70°.

Question illustration
A
1.8 meters
B
3.7 meters
C
15.2 meters
D
18.8 meters
2
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The angle measures associated with which set of ordered pairs share the same reference angle?

A
(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option B
C
(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
3

Circle D is shown. Angle A C B intercepts arc A B. Arc A B has a measure of 76 degrees.

Question illustration
A
38°
B
76°
C
90°
D
152°
4

What is the approximate length of arc s on the circle below? Use 3.14 for . Round your answer to the nearest tenth.

Question illustration
A
14.1 in.
B
22.5 in.
C
42.3 in.
D
56.5 in.
5

Segments RT and SU are diameters of circle O.

Question illustration
A
258°
B
266°
C
274°
D
282°
6

Which equation represents the circle described?The radius is 2 units. The center is the same as the center of a circle whose equation is x2 + y2 – 8x – 6y + 24 = 0.

A
(x + 4)2 + (y + 3)2 = 2
B
(x – 4)2 + (y – 3)2 = 2
C
(x – 4)2 + (y – 3)2 = 2²
D
(x + 4)2 + (y + 3)2 = 2²
7

Which of the following best explains the value of on the unit circle below?

Question illustration
A
The length opposite the angle is the vertical distance from the x-axis on the graph.
Option A
B
The length adjacent to the angle is the vertical distance from the x-axis on the graph.
Option B
C
The length opposite the angle is the horizontal distance from the y-axis on the graph.
Option C
D
The length adjacent to the angle is the horizontal distance from the y-axis on the graph.
Option D
8

Which of the following are in the correct order from least to greatest?

A
, , 80°, , 38°
Option A
B
38°, 80°, , ,
Option B
C
38°, , 80°, ,
Option C
D
, 38°, 80°, ,
Option D
9

In circle T, ∠PTQ ≅ ∠RTS.

Question illustration
A
24°
B
33°
C
48°
D
66°
10

Which statements about circle O are true? Select three options.

A
The radius of circle O is 13.
B
The diameter of circle O is 34.
C
LP is a diameter of circle O.
D
∠LMP intercepts a semicircle.
E
The measure of arc LP is 90°.
11

Circle C is shown. Radius A has a length of r.

Question illustration
A
32
Option A
B
64
Option B
C
256
Option C
D
1024
Option D
12

Angle D is a circumscribed angle of circle O.

Question illustration
A
17 units
B
23 units
C
27 units
D
60 units
13

Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.

Question illustration
A
35°
B
70°
C
75°
D
140°
14

Circle L is shown. Line segments K L and M L are radii. The length of K L is 12. Angle M L K is 60 degrees. Sector M L K with a 60 degree angle is shaded.

Question illustration
A
12
Option A
B
24
Option B
C
120
Option C
D
144
Option D
15

A circle is shown. Secant A D and tangent E D intersect at point D outside of the circle. Secant A D intersects the circle at point B. The length of A B is a, the length of B D is 10, and the length of D E is 12.

Question illustration
A
12(a + 12) = 102
B
10 + 12 = a2
C
10(a + 10) = 122
D
10(12) = a2
16

In circle D, ∠EDH ≅ ∠EDG.

Question illustration
A
4 units
B
5 units
C
6 units
D
9 units
17

Circle A is shown. Tangents L M and N M intersect at point M outside of the circle. Arc L N is 270 degrees.

Question illustration
A
75°
B
90°
C
120°
D
135°
18

In circle O, and are diameters. The measure of arc AB is 55° and the measure of arc CD is 25°.

Question illustration
A
100°
B
125°
C
235°
D
280°
19

A circle is shown. Secants D E and A E intersect at point E outside of the circle. Secant D E intersects the circle at point C and secant A E intersects the circle at point B. The length of D C is 1, the length of C E is x + 4, the length of A B is 11, and the length of B E is x + 1.

Question illustration
A
2
B
3
C
6
D
7
20

In circle P, diameter QS measures 20 centimeters.

Question illustration
A
9.9 centimeters
B
19.9 centimeters
C
21.5 centimeters
D
43.0 centimeters

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