Introduction to Circles — Unit test Answers

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1
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is tangent to circle P at point Q.

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A
37°
B
53°
C
90°
D
97°
2
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Line EF is tangent to circle G at point A.

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A
90°
B
95°
C
190°
D
195°
3

Two chords intersect at a point inside a circle that is not the center of the circle. Which statement must be true?

A
The measures of each pair of opposite arcs sum to 180°.
B
Each angle measure is equal to the measure of the arc it intercepts.
C
The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs.
D
Each arc measure is equal to one-half the sum of the vertical angles that intercept the arc.
4

In quadrilateral QRST, measures (5x+15)°. Angle TQR measures (4x+3)°.

Question illustration
A
15°
B
75°
C
105°
D
165°
5

Circle K is shown. Tangents S T and U T intersect at point T outside of the circle. A line is drawn from point T to point R on the opposite side of the circle. It goes through center point K. Lines are drawn from points S and U to center point K.

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

Circle R is shown. Tangents F G and H G intersect at point G outside of the circle to form an angle with a measure of 50 degrees. Point E is on the second arc. Arc F H has a measure of x degrees.

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A
130°
B
230°
C
260°
D
310°
7

Circle Y is shown. Chords R T and S U intersect. Arc R S is 106 degrees. The angle that intercepts arc R S is 94 degrees.

Question illustration
A
82°
B
100°
C
106°
D
118°
9

Circle B is shown. Line segments C B, D B, and E B are radii. Angle C B E is 52 degrees and angle E B D is 160 degrees.

Question illustration
A
106°
B
108°
C
148°
D
212°
10

In circle O, and are diameters. Arc ED measures 17°.

Question illustration
A
107°
B
180°
C
253°
D
270°
11

Circle O is shown. Tangents B C and B A intersect at point B outside of the circle. The measure of the first arc formed is 146 degrees.

Question illustration
A
34°
B
45°
C
68°
D
73°
12

The chords intersect at point U.

Question illustration
A
2
B
4
C
6
D
8
13

Which circle has a central angle that measures 40°?

A
Circle U is shown. Line segment Z X is a diameter. Line segment V X is a secant. Angle V X Z is 40 degrees.
Option A
B
Circle U is shown. Line segments U V and U Z are radii. Angle V U Z is 40 degrees.
Option B
C
Circle U is shown. Line segment Z V is a secant. Line segment Z X is a tangent. Angle X Z V is 40 degrees.
Option C
D
Circle U is shown. Line segments X V and X Z are secants. Angle V X Z is 40 degrees.
Option D
14

Which circle shows that measures 60°?

Question illustration
A
Circle O is shown. Line segments A and B are shown. The angle between the 2 segments is 60 degrees.
Option A
B
Circle O is shown. Line segment A is a tangent and line segment B is a secant. The angle between lines A and B is 60 degrees.
Option B
C
Circle O is shown. Line segments A O and B O are radii. Angle A O B is 60 degrees.
Option C
D
Circle O is shown. Line segment A Y is a secant. Line Y B is a diameter. Angle A Y B is 60 degrees.
Option D
15

Arc QVT measures 156°.

Question illustration
A
Angles QRT and QST both measure 78°.
B
Angles QRT and QST both measure 156°.
C
Angle QRT measures 78° and angle QST measures 102°.
D
Angle QRT measures 156° and angle QST measures 24°.

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