Review Ch. 10
Complete all problems on a separate sheet of paper.
Be sure to number each problem. Good Luck!
Problem #1
Find the exact length of arc AB, if circle
P has a radius of 18cm.
A
P 100°
B
Solution to #1
Arc Length = (100/360) * 36π
= (5/18) * 36π
= 10π cm.
Problem # 2
Find the diameter of a circle in
which a 36 cm chord is 80 cm
from the center.
Solution to #2
18cm
18cm
r
80cm
This is a 9, 40, 41 triangle times 2 so r =
82cm  diameter = 164 cm.
Problem #3
Find the radius of a circle
with a circumference of
20
Solution to #3
Circumference = π * diameter  so the
diameter must be 20  so radius = 10.
Problem #4
Find the measure of arc AE.
200о
A
B
x
210о
D
E
C
Solution to #4
*Arc BC = 360 – 210 = 150о
*Angle BDC is supp (tangent-tangent) = 30о
*So Angle ADE = 30о
*So 30 = (1/2)(200 – x)
60 = 200 – x
x = 140о
Problem #5
In the circumscribed polygon, find the
length of the AB.
15
A
10
12
B
Solution to #5
AB = 15 – (10 – x) + 12 – x
= 5 + x + 12 – x
10 - x
= 17
15 - (1 0 - x)
A
15 - (1 0 - x)
10 - x
x
12 - x
x
12 - x
B
Problem #6
In circle O, AB is a diameter.
OA=3x+5 and OB=2(5x-1).
Find AB.
Solution to #6
OA and OB are both radii so are equal.
3x + 5 = 2(5x – 1)
3x + 5 = 10x – 2
7 = 7x
1=x
each radius = 8 ; so diameter AB = 16
Problem #7
Solve for x if mA  5 x  6
B
and if mBC  12x  2
C
A
Solution to #7
Since angle A is inscribed;
2(5x + 6) = 12x – 2
10x + 12 = 12x – 2
14 = 2x
x=7
Problem #8
MATH is inscribed in the circle.
Angle M has a measure of 78 degrees.
Find the measure of angle T.
A
M
T
H
Solution to #8
Opp. Angles of inscribed quadrilaterals are
supp.
Measure of Angle T = 180 – 78 = 102о
Problem #9
Find the radius of the circle if AB is a
diameter, mAC  120 , and BC=20.
B
C
A
Solution to #9
*Measure of Angle B = 120/2 = 60
*Measure of Angle C = 90
*30 – 60 – 90 triangle with x = 20 ; so
diameter is 2x = 40
*Radius of AB is 20.
B
60
20cm
C
30
A
120
Problem #10
A circle is inscribed in triangle ABC.
AB=14, AC=12 and BC=4. Find BD.
A
B
C
D
Solution to #10
A
14 – x + 12 – x = 4
26 – 2x = 4
22 = 2x
x = 11
x
x
12 - x
14 - x
So BD = 14 – x = 3
B
14 - x
D
12 - x
C
Problem #11
A circle has a radius of 50.
How far from the center is a
chord of length 28?
Solution to #11
7, 24, 25 right triangle
14
14
x
So x = 2 * 24 = 48
50
Problem #12
A regular octagon is inscribed
in a circle.
What is the measure of an arc
cut off by a side of the
octagon?
Solution to #12
* Regular - so all chords congruent.
* Congruent chords = congruent
arcs.
360/8 = 45о
Problem #13
Two concentric circles have radii of
lengths 16 and 20. Find the length of a
chord of the larger circle that is
tangent to the smaller circle.
Solution to #13
• 3, 4, 5 right triangle
20
x = 12 so length of the chord
is 24.
x
16
Problem #14
A 12 by 10 rectangle is inscribed
in a circle. Find the radius.
Solution to #14
• 144 + 100 = c2
244 = c2
244 = c
2 61 = diameter
so radius = 61
10
12
Problem #15
Two secants drawn to a circle from an
external point intercept arcs that are 122°
and 68°. Find the measure of the secantsecant angle.
122°
68°
P
Solution to #15
• Angle P = (1/2)(122 – 68)
= (1/2)(54)
= 27о
Problem #16
Find the circumference of a
circle in which an 80 cm chord
is 9 cm from the center.
Solution to #16
• 9, 40, 41 right triangle so r = 41
• C = 2π(41)
r
= 82 π cm
40
9
40
Problem #17
A central angle intercepts an arc that is 5/12
of the circle. Find the measure of angle x.
O
x
5
12
of circle O
Solution to #17
• If arc is 5/12  central angle is 5/12 of 360
so central angle is 150о
• Radii are congruent so isosceles triangle 
only 30о left.
• Angle x = 30/2 = 15о
Problem #18
If PA and PB are tangent to circle O at A
and B, PA=24, and PO=26, find
perimeter of quadrilateral PAOB.
A
O
P
B
Solution to #18
• OA is perpendicular to PA  5, 12, 13 right
triangle.
• OA = 10 and PB = 24
• 10 + 10 + 24 + 24 = 68
Problem #19
Find the measure of angle x.
x
92°
44°
Solution to #19
? = (1/2)(44 + 92)
? = (1/2)(136)
? = 68
44
x = 180 - 68
x = 112
x
92
?
Problem #20
What is the length of a chord that
cuts off an arc of 120 degrees in
a circle with a radius of 8?
Solution to #20
30, 60, 90 triangle
2x = 8
x=4
Chord = 2(4 3)
=8 3
x 3
8
60
Problem #21
Parallelogram ABCD is inscribed in
circle Q, with dimensions of 24 by
10. Find the area of circle Q.
Solution to #21
24
Parallelogram inscribed
is a rectangle.
Diameter = 26
radius = 13
Area = (132) = 169
10
Problem #22
Circle A has a radius of 5 inches, and
circle B has a radius of 20 inches. The
centers are 39 inches apart. Find the
length of the common external tangent
D
(CD).
C
•
•
B•
•
A
Solution to #22
Rt. Triangle is 5, 12, 13 so
AE = 12(3) = 36 in. So
then CD = 36 in.
D
C
5 in
5 in
E
15 in
B
A
39 in.
Problem #23
Two tangent segments of a circle with a
diameter of 50 inches form a 60 degree
angle where they meet at P. How far is
P from the center of the circle?
P
60°
Solution to #23
If  P = 60, then mAB = 120,
so ACB = 120. PC bisects
ACB so ACP = 60. We
have a 30-60-90 triangle with
x = 25 in.
A
PC = 50in.
P
25 in
30
60
B
C
Problem #24
AB & AC are tangent to the circle.
Find the measure of arc BDC.
B
A
D
76°
C
Solution to #24
Minor arc supp. to angle = 104
B
mBDC = 360 - 104 = 256
D
A
76
104
C
STUDY!!!!!