Download Date - White Plains Public Schools

Mr. Laporte
Student Name:
Worksheet
1. A peach pie is made with 13 peaches which are
evenly distributed throughout the pie. If Joe
eats one slice of pie that is big enough so that he
eats exactly 5 peaches, what was the angle of the
slice to the nearest tenth of a degree?
Geometry
Date:___
6. In the accompanying diagram of circle O, AB
and BC are chords and maAOC = 96. What is
maABC?
2. In a circle with a radius of 4 centimeters, what is
the number of radians in a central angle that
intercepts an arc of 24 centimeters?
3. In a circle whose radius is 2, a central angle
intercepts an arc whose length is 6. What is the
number of radians in the central angle of the arc?
(1) 32
(2) 48
(3) 96
(4) 192
7. In the accompanying diagram of circle O,
m´B¼ = 150.
4. In a circle whose radius is 9 centimeters, what is
the number of radians in a central angle if the
length of the intercepted arc is 18 centimeters?
5. Two tangents are drawn to circle O from
external point P. If the major arc formed has a
measure of 280º, find maP.
Circles & Angles
What is maABC?
(1) 210
(2) 105
Page 1
(3) 95
(4) 75
Mathematics
Mr. Laporte
Student Name:
Worksheet
8. The new corporate logo created by the design
engineers at Magic Motors is shown in the
accompanying diagram.
If chords BA and BC are congruent and
mµ¼ = 140, what is maB?
(1) 40
(3) 140
(2) 80
(4) 280
Geometry
Date:___
10. In the accompanying diagram of circle O,
tangent PB, secant AECP, chord DEB, and
chord CB are drawn; m·¼ = 90; maDEC = 85;
BP = 15; and CB = 8.
Find:
a m´»
b maACB
c maP to the nearest degree
9. In the accompanying diagram of circle O, chords
AB and CD intersect at E, m´¼ = 50, and mµ½
= 150. Find maAED.
11. In the accompanying figure of circle O,
maAOC =52. Find maABC.
Circles & Angles
Page 2
Mathematics
Mr. Laporte
Student Name:
Worksheet
Geometry
Date:___
12.
Find the measure of aP, in degrees, and find the length of rod PT, to the nearest tenth of a centimeter.
13. In the accompanying diagram of circle O, XA[
and XB[ are tangents and maXAB = 75. Find
maX.
15. In the accompanying diagram of circle O,
maAOC = 108.
What is maABC?
(1) 27
(2) 54
(3) 108
(4) 216
14. In a circle, an inscribed angle intercepts an arc
whose measure is (14x ‚ 2)º. Express, in terms of
x, the number of degrees in the measure of the
inscribed angle.
Circles & Angles
Page 3
Mathematics
Mr. Laporte
Student Name:
Worksheet
16. The accompanying diagram shows a child's spin
toy that is constructed from two chords
intersecting in a circle. The curved edge of the
larger shaded section is one-quarter of the
circumference of the circle, and the curved edge
of the smaller shaded section is one-fifth of the
circumference of the circle.
What is the measure of angle x?
(1) 40º
(3) 81º
(2) 72º
(4) 108º
Geometry
Date:___
18. In the accompanying diagram, CD is tangent to
circle O at B, AO and BO are radii, and chord AB
is drawn. If maAOB = 108, find maABD.
19. In the accompanying diagram, AB and AC are
tangents to circle O, and chord BC is drawn. If
maABC = 72, what is maA?
17. In the accompanying diagram of circle O, the
measure of inscribed angle BAC is 40º. Find, in
degrees, the measure of central angle BOC.
Circles & Angles
Page 4
Mathematics
Mr. Laporte
Student Name:
Worksheet
Geometry
Date:___
20. In the diagram below, PA is tangent to the circle
at A and PBC is a secant. If m´» = 80 and
mµ¼ = 100, what is maAPB?
22. In the accompanying diagram of circle O, chord
AB is parallel to chord CD. If m´¼ = 100, find
maBOD.
21. In the accompanying diagram of circle O, the
ratio of µ¼ to ´» is 2:1.
23. In the accompanying diagram, isosceles triangle
ABC is inscribed in the circle. If AB ? CB and
m´» = 150, find maB.
What is maACB?
(1) 30
(2) 45
Circles & Angles
(3) 60
(4) 90
Page 5
Mathematics
Mr. Laporte
Student Name:
Worksheet
24. In the diagram below, chords AB and CD
intersect at E. If maAEC = 4x, m´¼ = 120, and
m·» = 2x, what is the value of x?
(1) 12
(2) 20
26. Quadrilateral ABCD is inscribed in circle O. BD
and AG are diameters, PAB and PDC are
secants, m´½ = 80, and m·¼ = 40.
(3) 30
(4) 60
25. In the accompanying diagram, BD[ is tangent to
circle O at B. BC is a chord, and BOA is a
diameter. If m´¼:m¶» = 1:4, find maDBC.
Circles & Angles
Geometry
Date:___
Find:
a m´»
b maBCD
c maBOG
d maP
e maBAG
Page 6
Mathematics
Mr. Laporte
Student Name:
Worksheet
27. In the diagram below, PA is tangent to circle O,
and AB is a chord. If m´C» = 300, find the
measure of aBAP.
Geometry
Date:___
29. In the accompanying diagram, quadrilateral
ABCD is inscribed in circle O. If m´» = 132 and
mµ¼ = 82, find maADC.
28. In the accompanying diagram, chord CD is
parallel to diameter AB. If m´¼ = 25, what is
maCOD?
30. In the accompanying figure, (ABC is inscribed in
circle O, AB is a diameter of circle O, AB = 20,
BC = 16, and the measure of minor arc
AC = 74.
(1) 25
(2) 65
(3) 130
(4) 155
a Find the measure of aACB.
b Find the measure of aBAC.
c Find the length of AC.
d Find the area of (ABC.
e Find the area of circle O. [Answer may be left
in terms of p.]
Circles & Angles
Page 7
Mathematics
Mr. Laporte
Student Name:
Worksheet
31. Using the accompanying figure, where (ABC is
inscribed in circle O, BT bisects aCBA, TA[ is
tangent to circle O, and
maBAC:maCBA:maACB = 2:3:4.
Find:
a maBAC
b mµ¼
c maCPT
d maPAT
e maT
Circles & Angles
Geometry
Date:___
32. In the accompanying diagram, AB is a diameter
of circle O, the measure of aBAC is 40, and the
measure of ´½ is 70.
a Find the measure of minor arc BC.
b Find maBOC.
c Find maACD.
d Find the measure of minor arc CD.
e Find maAOC.
Page 8
Mathematics
Mr. Laporte
Student Name:
Worksheet
33. In the accompanying diagram, AC and BD are
diameters of circle O and the measure of aACB
is 50.
a Find the measure of minor arc AB.
b Find maBOC.
c Find maBAC.
d Find the measure of minor arc AD.
e Find maABC.
Circles & Angles
Geometry
Date:___
34. In the diagram below, PR is a diameter of circle
O. The measure of aQOR is (4x ‚ 10)º and the
measure of aQOP is (x + 50)º.
a What is the value of x?
b How many degrees are in the measure of
minor arc QP?
c How many degrees are in the measure of
aQRP?
d If the area of circle O is 16π, find the
circumference in terms of π.
Page 9
Mathematics
Mr. Laporte
Student Name:
Worksheet
Geometry
Date:___
35. In the diagram below, (ABC is inscribed in circle
O. Triangle ABC is isosceles with AB ? BC.
Line EF, which contains point B. is parallel to
line AC. The degree measure of arc BC is 150.
a the measure of aBAC
b the measure of aEBA
c the measure of aABC
d the measure of arc AC
e the measure of aABF
Circles & Angles
Page 10
Mathematics
Worksheet
Answer Key
[New Exam]
1. 138.5°
25. 72
2. 6
26. a 100; b 90; c 80; d 30; e 40
3. 3
27. 30
4. 2
28.
5. 100
29. 107
3
6.
2
30. a 90; b 53; c 12; d 96; e 100p
7.
2
31. a 40; b 80; c 110; d 60; e 50
8.
1
32. a 80; b 80; c 35; d 30; e 100
9. 80
33. a 100; b 80; c 40; d 80; e 90
10. a 80; b 40; c 20
34. a 28; b 78; c 39; d 8p
11. 26
35. a 75; b 75; c 30; d 60; e 105
12. 80 and 9.2
13. 30
14. 7x - 1
15.
2
16.
3
17. 80
18. 54
19. 36
20. 50
21.
1
22. 100
23. 30
24.
2
Circles & Angles
Mathematics
Question ID's in Numerical Order.
1. 130
2. 157
3. 187
4. 234
5. 261
6. 2075
7. 2082
8. 2089
9. 2096
10. 2097
11. 2126
12. 2133
13. 2158
14. 2169
15. 2171
16. 2174
17. 2186
18. 2215
19. 2232
20. 2238
21. 2248
22. 2257
23. 2263
24. 2265
25. 2270
26. 3641
27. 3662
28. 3674
29. 3738
30. 3848
31. 3938
32. 4127
33. 4211
34. 4225
35. 4430
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