Practice Semester Exam: 2014-2015
Unit 8 Questions
8.1-1) Draw two circles of different radii. Prove the circles are similar.
8.1-2) Use the diagram.
s
D
r
C
To show circle C is similar to circle D, one would have to translate circle C by the vector CD . Then,
circle C would have to be dilated by what factor?
(A) s  r
(B) s 2  r 2
s
(C)
r
s2
(D) 2
r
In questions 3-4, use the diagram of two concentric circles centered at O, and mAOB  70 .
A
E
H
O
D
F
B
8.2-3) ADB is called a major arc.
(A) True
(B) False
8.3-4) mAB  mEF
(A) True
(B) False
8.5-5) Use the figure.
A
D
C
B
Quadrilateral ABCD is to be circumscribed by a circle. What must be true?
(A) Opposite angles are supplementary.
(B) One of the angles is a right angle.
(C) Both must be true.
(D) Neither must be true.
In questions 6-7, use the diagram of a scalene triangle where M is the midpoint of AB .
k

g
C
h
B
A
M
8.6-6) The incenter of ABC lies on which line?
(A) g
(B) h
(C) k
(D) 
8.6-7) The centroid (center of mass) of ABC lies on which line?
(A) g
(B) h
(C) k
(D) 
In question 8, use the diagram where Circle 1 is circumscribed about ABC and Circle 2 is inscribed in ABC.
B
Circle 1
Circle 2
C
A
8.6-8) To find the center of Circle 2, what would be constructed on ABC?
(A) altitudes
(B) angle bisectors
(C) medians
(D) perpendicular bisectors
8.6-9) Inscribe a circle in the triangle below by construction.
B
C
A
In question 10, use the diagram of a scalene triangle where M is the midpoint of AB .
k

g
C
h
B
A
M
8.7-10) The circumcenter of ABC lies on which line?
(A) g
(B) h
(C) k
(D) 
In question 11, use the diagram where Circle 1 is circumscribed about ABC and Circle 2 is inscribed in ABC.
B
Circle 1
Circle 2
C
A
8.7-11) To find the center of Circle 1, what would be constructed on ABC?
(A) altitudes
(B) angle bisectors
(C) medians
(D) perpendicular bisectors
8.7-12) Circumscribe a circle in the triangle below by construction.
B
C
A
8.9-13) Use the diagram.
130°
K
60°
N
L
90°
M
What is mNKM ?
(A) 30°
(B) 45°
(C) 60°
(D) 90°
8.9-14) In circle O, mQPT  42 .
P
Q
42°
O
T
R
What is mQRT ?
(A) 21º
(B) 42º
(C) 63º
(D) 84º
8.9-15) WY is a diameter of circle C. mZCY   2 x  10  , mWCZ   4 x 10  , and mYCX   2 x  4  .
Y
Z
X
C
W
What is the value of x?
(A) 22
(B) 30
(C) 32.5
(D) 43.5
8.9-16) In circle O, mRQP  82 .
Q
P
82°
O
T
R
What is mRTP ?
(A) 41°
(B) 82°
(C) 98°
(D) 164°
8.9-17) Use circle J.
L
5x  15 
120
J
K
What is the value of x?
(A) 9
(B) 21
(C) 27
(D) 45
In questions 18-19, use the diagram below where KM and KN are tangent to circle O.
M
K
O
50°
L
N
8.9-18)What is mMON ?
(A) 50°
(B) 80°
(C) 90°
(D) 100°
8.9-19)What is mKMO ?
(A) 50°
(B) 80°
(C) 90°
(D) 100°
In question 20, use the diagram of two concentric circles centered at O, and mAOB  70 .
A
E
H
O
D
F
B
8.9-20) mEF  70
(A) True
(B) False
In questions 21-22, the segments DB and DC are tangent to circle A.
C
D
A
B
8.10-21)  BCD is a right triangle
(A) True
(B) False
8.10-22) BD = CD
(A) True
(B) False
In questions 23-25, AB is tangent to circle D at A, and BC is tangent to circle D at C.
A
r
E
B
D
C
8.10-23) AB = CB
(A) True
(B) False
8.10-24)  AB   r 2   BD 
(A) True
(B) False
2
8.10-25)  BE  BD    BC 
(A) True
(B) False
2
2
8.10-26) An astronaut stands at the peak of a mountain on a distant planet. The planet has a diameter of 4000
km and the distance from the peak to the horizon is about 210 km. (When looking to the horizon, one’s line
of sight is tangent to the surface of the planet.)
210 km
4000 km
How tall is the mountain? (Diagram not drawn to scale.)
8.10-27) What is the equation of the line tangent to the circle x 2  y 2  32 at (4, 4)?
8.11-28) In the diagram, mKN  25 and mML  65 .
P
K
25°
N
L
65°
What is mKPN ?
(A) 20°
(B) 25°
(C) 45°
(D) 65°
M
8.11-29) Use the diagram.
A
B
E
4 mm
3 mm
4 mm
C
What is AC?
1
(A) 5 mm
3
(B) 8 mm
1
(C) 8 mm
3
(D) 16 mm
D
For questions 30-31, use circle O where mMHJ  120 , and points H and O are distinct.
K
J
H
O
M
L
8.11-30) mJM and mKL could be 100° and 140°, respectively.
(A) True
(B) False
8.11-31) mJM and mKL could both be 120°.
(A) True
(B) False
8.11-32) In circle O, mMHL  x and mJK  40 .
K
M
O
40
H
J
L
What is mLM ?
(A) 40
(B)  x  20  
(C)
(D)
x
 x  40 
 2x  40 
8.11-33) In circle O, mJL   6 x  5  , mKM  10 x  3  , and mJHL  140 .
K
M
O
H
J
L
What is the value of x?
(A) 8.25
(B) 9.25
(C) 17
(D) 18
8.11-34) In the figure below, mJK  26 and mMN  130 .
M
J
H
O
K
N
What is mH ?
(A) 52°
(B) 78°
(C) 104°
(D) 128°
8.11-35) In the figure below, mAB  m and mCD  n .
E
C
D
O
B
A
What is mE ?
(A) m  n
1
(B)  m  n 
2
(C) m  n
1
(D)  m  n 
2
8.11-36) In the figure below, mJK  66 and mMN  128 .
M
J
H
L
O
K
N
What is mH ?
(A) 31°
(B) 62°
(C) 64°
(D) 97°
8.11-37) In circle C, UW = XZ, VW = 2x + 14, and YZ = 6x +2
W
V
X
U
C
Y
Z
What is the value of x?
(A) 2
(B) 3
(C) 4
(D) 5
In question 38, the segments DB and DC are tangent to circle A.
C
D
A
B
1
mBC  mBDC
2
(A) True
(B) False
8.11-38)
In questions 39-41, CD is perpendicular to chord AB in circle C.
B
D
A
C
8.11-39) AD = BD
(A) True
(B) False
8.11-40) CD = BD
(A) True
(B) False
8.11-41) AC = CB
(A) True
(B) False
8.11-42) With respect to circle D, AB is tangent at A, and CB is tangent at C.
A
12
B
D
16
C
What is the length of BD ?
(A) 11
(B) 14
(C) 16
(D) 20
8.11-43) Use the figure.
P
R
7
4
S
T
What is the length of RP ?
(A) 9
(B) 11
(C) 28
(D) 77
8.11-44) In the diagram below KM and KN are tangent to circle O, and ML = NL.
M
K
O
50°
N
What is mONL ?
(A) 15°
(B) 25°
(C) 65°
(D) 90°
L
In questions 45-46, use the figure.
AC and BC are secants of the circle and FC is tangent, where AB = 20, BC = 4, and CD = 3.
F
A
C
B
D
E
8.11-45) What is DE?
(A) 15
(B) 18
(C) 29
(D) 32
8.11-46) What is FC?
(A) 12
(B) 40
(C) 80
(D) 96
In question 47, use the diagram below where KM and KN are tangent to circle O.
M
K
O
50°
L
N
8.11-47)What is mMKN ?
(A) 50°
(B) 80°
(C) 90°
(D) 100°
8.12-48) (HONORS) Construct a line tangent to circle O that passes through point A.
O
A