Module 5: Review Worksheet Aims 1-17
Work on loose-leaf!
1a) Name a central angle.
b) Name an inscribed angle.
c) Name a chord that is not a diameter.
d) What is the m≮CAD?
e) What is m≮CBD?
f) Name 3 angles of equal measure.
g) What is the degree measure of CDB ?
h) Name a minor arc.
i) Name a major arc.
0
2. If m≮CAD = 50 ,
a) mCD = ________
b) mCBD = ________
c) m≮CBD= _______
0
0
3. In the figure, m≮BCD = 74 and m≮BDC = 42 .
K is the midpoint of CB, and J is the midpoint of
BD. Find m≮KBD and m≮CKJ.
4. Find the value of x.
b)
a)
e)
f)
c)
g)
d)
h)
5. a. Give the center, radius, circumference and area of the circle whose
2
2
equation is x - 6x + y - 8y = 38 [circumference and area in terms of Π]
b. Given the equation (x - 2)(x - 6) + (y - 5)(y + 11) = 0, what is the center
and radius?
c. Determine the equation of the line tangent to the circle
2
2
x + y - 2y + 6x - 7 = 0 at the point F(-2,5).
6. Give the center and radius (simplest radical form) of the circle whose equation is:
2
2
2
2
a. (x - 6) + (y - 3) = 25
b. x + (y - 5) = 50
2
2
2
2
c. x + y = 28
d. (x + 2) + y = 18
2
2
2
2
e. (x + 7) + (y - 10) = 24
f. 3x + 3y = 144
7. BC is tangent to circle A at point B. DC = 9 and BC = 15.
a. Find the radius of the circle.
b. Find AC.
0
8. In circle A, BC is a diameter and CE = 68 .
a) Find mCD.
b) Find m≮DBE.
c) Find m≮DCE.
9.
and EF = 12. Find AC.
10. Two concentric circles have radii of 6 and 14. Chord BF of the larger circle
intersects the smaller circle at C and E, CE = 8 and
.
Find AD and BF in simplest radical form.
11. In the diagram below, circles X and Y have two tangents drawn to them from
external point T. The points of tangency are C, A, S, and E. The ratio of TA to AC
is 1:3. If TS = 24 find the length of SE.
0
12. P and Q are points on a circle of radius 9 cm, and the measure of PQ is 120 .
a) Find the length of PQ in terms of pi.
P
b) Find the ratio of the arc length to the radius of the circle
(the radian measure of angle ≮POQ).
P
c) Find the length of PQ in simplest
radical form.
O
Q
Q
O
d) Find the distance from chord PQ to the center of the circle.
e) Find the perimeter of sector POQ in terms of pi.
f) Find the exact area of the wedge between chord PQ and PQ (the segment).
g) Find the perimeter of this wedge
13. An arc of a circle has length equal to the diameter of the circle. What is the
measure of that arc in radians? Explain your answer.
14. Two circles have a common center O. Two rays from O intercept the circles
at points A, B, C, and D as shown. Suppose OA and OB are in a ratio of 2:5 and that
2
the area of sector AOD is 10 cm .
a. What is the ratio of the measure of the arc AD to the
measure of the arc BC?
b. What is the area of the shaded region?
c. What is the ratio of the length of the arc AD to the
length of the arc BC?
o
15. a) Express an angle of 75 in radians.
b) Express an angle of 5π
in degrees.
36
16. Circle O has a diameter of 18. Central angle θ intercepts an arc with a length of
15π. Find the measure of angle θ in radians and in degrees.
17. Given: Circle O with diameters MOT and AOH.
Prove MA ≅ TH
M
A
O
H
T
18. Find the missing variables:
400
500
a)
x
b)
O
300
c)
y
2100
O
x
x
300
x
d)
y
O
400
1900
O
1900
550
e)
f)
g)
600
x
O
x0
BC is a diameter. x
x
h)
i)
j)
<
<
O
(9x)o
2x
(3x)o
O
o
50
3x
y
1400
k)
l)
m)
x
O 1400
y
x
y
n)
o)
C
19. Write the equation for the circle:
y
20. Rays PA and PB are tangent to circle O at points A and B respectively. Diameter
0
0
BOD and chord AC intersect at E. The mCB = 160 and the m≮APB = 40 . Find:
a) mAB
b) mDA
c) mCD
d) mADCB
e) m≮DEC
f) m≮PAC
g) m≮PBD
h) m≮PBA
D
C
A
E
O
P