O IS THE CENTER OF THE CIRCLE, OBCD IS A RECTANGLE AB=3 BD=5
FIND THE RADIUS OF THE CIRCLE
A
3
C
B
5
E
O
D
A
B
C
AE BC; AD  2; BC  8
O IS THE CENTER OF THE CIRCLE
D
Find AE
O
E
GIVEN: O; BO PS ; OC QR
Chords PS & QR are equidistant from the center of O
PROVE: PQ  SR
Q
P
C
B
O
R
S
A
P
GIVEN: O; OC  OQ
OC BP; OQ AM
D
PBMAMB
PROVE: CD  DQ
Q
C
O
M
B
O
OB bisects QS
BT=8
RT=BP=2
Find ST and AO
A
O
R
2
B
Q
T
2
P
S
B
P
Q
Given O, BC=5, PQ=30 BO PQ
C
Find the radius of O
O
Given O with radius 12 and AB=12;
OP AB Find OP
A
P
B
O
O
has radius 12. How far from the center of the circle is a chord
with length 12?
AD, AB, BC,& DC are tangents
AB=30; BC=20; DC=14 Find AD
B
P
K
A
T
C
W
D
O has radius 10
P has radius 7
O is tangent to P
ST is tangent to both
Find the length of ST
T
S
P
O
THE WALKAROUND PROBLEM
FN=20; NU=14, FU=12
F,U, & N are tangent
to each other.
Find the radii of all three
circles.
20
N
F
14
12
U
THE COMMON EXTERNAL TANGENT PROBLEM
The radius of E=12. The radius of A=8. EA=40
YS is tangent to both circles. Find its length
A
E
S
Y
THE COMMON INTERNAL TANGENT PROBLEM
A
H
D
is tangent to A and
H. HA=40
The radius of A is 8
The radius of H is 12
Find RD
RD
R
Two circles with radii 8 and 4 are externally tangent. Find
the length of the common tangent segment.
C,U & B are
tangent.
CU=28
CB=22
BU=25
C
U
Find the radius
of C
B
CD AF
CD is a diameter
mA=30
AB=13
GD=1
Find CD and EA.
C
B
G
F
E
D
A
Given Semicircle W,
TA=4,
ST = 6
ST  BA
Find the diameter of the semicircle.
S
B
W
T
A
A
C
B
O
S
D
O has radius 12,
S has radius 9
OS=28
Find the length of
the external and
internal common
tangent segments
to the two circles.
ST is tangent to both s.
The radius of A=4
The radius of B=9
Find SM
T
S
M
A
B
Q
P
R
PQR is
equilateral
Its sides are
tangent to the
sides of the
smaller of the
two concentric
circles. If the
radius of the
larger circle is
12, find the
radius of the
smaller circle.
mGKD = 80; mR=32; BG  AD Find the measure of all
arcs and angles in the diagram
B
G
K
A
R
D
BIG CIRCLE




mJ I  62 ; Ma  32 ; mBJ  24 EG is tangent to O at F
E
D
C
B
24
32
O
J
F
62
K
G
I
H
mEDC 
mFAC 
mEFC 
mOCA 
mCDF 
mFOH 
mCFA 
mOKI 
mGFI 
mACF 
mFJI 
mJIF 


mCF 

mFH 
mCB 

mHI 

mJ FH 
A
IKMJ is a parallelogram JM = 8 ; JI = 10 Find the diameter of the circle
J
M
I
K
mA  40
mB  100
B
A
mC 
C
mD 
D
B
AC is a diameter of the circle
AB = 12
mDC  40

D

E
A
F
G
C
mAG  80
AB  DG
Find the diameter of the circle and
the measure of all arcs.
Find any other thing you can. Can
you determine EF?
Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square., and the
tangent to the semicircle from C intersects side AD at E. What is the length of
D
CE ?
C
E
A
B
Circles A,B and C are externally
tangent to each other and
internally tangent to circle D.
Circles B and C are congruent.
Circle A has radius 1 and passes
through the center of D. What is
the radius of circle B?
B
A
D
C
 
AB is a diameter; AB = 12; AD  BD ; EA  EC
Find BC, DC, DB & DE
C
E
D
B
A
ABC is drawn in a circle so AC is a diameter and CAB=60. B is on the circle.
AB = 10. Find the diameter of the circle and the length of BC
A regular hexagon is inscribed in a circle. Each side of the hexagon is 6. Find the
diameter of the circle and the distance from the center of the circle to one edge of the
hexagon.
A regular octagon is inscribed in a circle. Each side of the octagon is 8. Find the diameter
of the circle and the distance from the center of the circle to one edge of the octagon.
A regular decagon is named A1 A2 A3 ... A10 .
Find each angle
mA1 A5 A2 
mA2 A5 A4 
mA10 A1 A2 
Diagonals A1 A4 and A5 A2 intersect at B
Find mA2 BA4
The endpoints of the diameter of a circle are the x and y intercepts
of the line with equation 4 x  3y  24 . Find the radius of the circle
and decide if the circle passes through the origin.
A
B
C
CD is tangent to the circle
BD AC ; AB=16
The radius of the circle is 10
Find CD, BD
D


O is the center of both AB and CD
OC OD ; AC=8
O
A
C

Find the length of OB
B
D

The length of CD = the length of AB
ABC is equilateral, AC  12 3 cm.
Find the length of AB

A
B
C
P
A
90
C
mPAC=90
A is the center
PA=8
Find the total perimeter of the figure
20
12
20
The curved pieces on either
end are semicircles. Find
the total perimeter.
P
S
O
R
Q
PQ=24
PQ is a
diameter of O
PS is tangent
to O at P
mQPR=30
PS=
PR=
RS=
U
Find mN and mL
80
N
120
V
L
The two circles are concentric
with center O. CB is tangent to
the smaller circle. The radii of the
two circles are 6 and 12.
Determine the length of
P
C
B
F
O
E
D
PE, DC, and BC
The two circles are concentric with center O.
Find the length of
CB is tangent to the smaller circle at P. PS  5, ST  4
CB
Q
P
B
C
O
S
T
A & B are externally tangent. DF is the common internal tangent
C
D
E
A
F
B
The radius of
A is 8.
The radius of
B is 2
Find
CE,DF,BD,DA,
mCFE (draw
it in ) mADB
and CF
A
The circles are
concentric and
are inscribed in
squares.
AB=16
Find the
circumference of
the smallest
circle pictured
B
POWER
TM=3
MW=4
MS=12
Find PM

P
T
3
M
W
4
12

FT is tangent
FT=8 ;KT=6
Find RT

R
F
K
8
6
S
T
A
4
B
8
C
BC=8
DC=6
AB=4
Find ED
6
D
E
KW=KM=6
NR=1
Find RW
N
1
M
R
6
K
6
W
Determine x,y,z,w,s and m
y
58
x
23
w
26
48
z
38
114
m
88
s
52
88
104
C
F
80
80
A
D
1.  O
mBC  80
x

60
H
Find mCAB
O
B
G
E

4. O, mDE  60
mFG  80
Find
mD,mF,mDHE

R
T

2. O
mTP  120
Find mS
L
120
40
S
O
M
P
  50
3mQS
Find mR

S

mMT  100
100

5.
mLSO, 40
T
Find mM,mR
and mMST
6 Find mC
and mFRW
C
R
Q
J
50
30
S
P
R
F
80
W
Please do these problems in numerical order.
A
Prove David’s Theorem
Given: O,P
OA tangent to P
AP tangent to O
Prove: AC bisects AOK
O
C
B
STATEMENTS














REASONS
K
P
Given: CD, AE , BE are each tangent to two circles
A is tangent to B at D
A is tangent to C at F
B is tangent to C at E
Prove:ABC is equilateral
B
D
E
A
F
STATEMENTS













REASONS
C