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Geometry Name
Chapter 12 Study Guide Period
1. Identify each of the following features (make sure to include
correct notation –
line, line segment, etc):
a. two chords:
b. a secant:
c. a tangent:
d. a diameter:
e. a radius:
2. For each part below, draw in a second (smaller) circle so
that the two circles are:
a) Concentric b) Internally tangent c) Externally tangent
3. Draw in two…
a) Common external tangents b) Common internal tangents
4. If BC is tangent to A at C, AD = 16 and BC = 30, find BD.
B
C
A D
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5. Given the diagram below, with AB = 6x - 5 , BC = 5x – 1, and
BD = 3x + 9, Find the
radius of the circle.
6. Given: A and 100CD , find
a) m CAB
b) The measure of major arc BDC
7. Given: O
PQ RS
6 10mPQ k
7 1mQR k
8 4mRS k
Find: m ROQ
8. Given: A
AC BD
AE = 9
EC = 7
Find: BD
B
C
A
D
B C
A
D
P
R S
O
Q
B C
A D
E 7
9
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9. A chord of length 48 inches is drawn in a circle of radius 26
inches. How far is the
chord from the center of the circle?
10. If A has a radius of 8 cm and 120m BAC , find
a) the area of sector CAB
b) the length of arc BC
c) the area of segment CAB
11. Central angle RTS is drawn in circle T of radius 6 inches.
If the area of sector
RTS is 8 in2, what is m RTS ?
12. A central angle of 72 intercepts an arc of length 10 inches.
What is the radius
of the circle?
B
C
A
9 cm
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13. Find the measure of CED
14. Find the measure of DGF
15. Find the measure of and ACB DC
16. In A as shown, if BC = 4 and AD = 5, find CD.
C
D
E
164
136
(15x+22)
G
F
D
(6x+2)
D
B
C
A (4x+8) (5x)
(8x-8)
B C
A
D
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17. In quadrilateral ABCD shown at right,
4 8m A z
13
2
zm B
3 10 m D z
Find m C .
18. Find mMN if 110mQP and 96m NRP
19. Find m 1 if 92mMN and 118mPQ .
20. Find m A given the arc measures as shown.
21. Find the value of x given the diagram as shown.
B C
A
D
92 M N
P Q
1
118
110
M N
P Q
R 96
A
79o
227o
A
(2x+3)o
(6x – 47)o
45o
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22. If BC is tangent to A at C, and 154mCD , find m BCD .
23. Write the equation of a circle with a center at 7, 5 and a
radius of 8.
24. Find the center and radius of the circle 2 2
2 11 50x y
Center
Radius
25. Find the equation of the circle having 4,2 and 2,10 as
endpoints of a diameter.
26. Complete the square to write the equation of the circle in
standard form, then
identify the center and radius of the circle: 2 2 12 8 3 0x y x
y
Equation:
Center:
Radius:
B
C
A D
154
