Name ———————————————————————
Date ————————————
Practice A
LESSON
10.5
For use with pages 708–714
If a tangent and a chord
intersect at a point on a
circle, then the measure
of each angle formed is
one half the measure of
its intercepted arc.
Find the measure of each numbered angle or arc.
1.
2.
172⬚
128⬚
2
1
1
4.
2
33⬚
2
1
131⬚
82⬚
1
5.
6.
1
2
47⬚
132⬚
41⬚
117⬚
If two chords intersect
inside a circle, then the measure
of each angle is one half the
sum of the measures of the arcs
intercepted by the angle and its
vertical angle.
1
ma1 5 }2 (1318 1 338)
ma1 5
ma2 1 ma1 5 1808
8
ma2 5
8
86⬚
2
1
7.
8.
2
1
92⬚
43⬚
1
270⬚
9.
138⬚
66⬚
1
If a tangent and a secant, two tangents,
or two secants intersect outside a circle,
then the measure of the angle formed is
one half the difference of the measures
of the intercepted arcs.
1
ma1 5 }2 (138° 2 66° )
212
Geometry
IDEA! Works
Copyright © Holt McDougal Math. All rights reserved.
LESSON 10.5
3.
Name ———————————————————————
Practice A
LESSON
10.5
Date ————————————
continued
For use with pages 708–714
10.
105⬚
130⬚
1
2
Since the tangent and a chord
intersect at a point on a circle,
then the measure of each angle
formed is one half the measure
of its intercepted arc.
3x 2 1 = }1 (5x 1 33)
70⬚
Find the value of x.
2
11.
12.
96⬚
LESSON 10.5
(3x 2 1)⬚
(5x 1 33)⬚
x⬚
13.
14.
x⬚
45⬚
x⬚
38⬚
Copyright © Holt McDougal Math. All rights reserved.
(10x 2 1)⬚
15. Theater A play is being presented on a circular stage.
The two main characters are at positions A and B at the
back of the stage. Use the diagram to answer the
following questions.
B
808
388
C
D
E
A
a. What angle of view between the main characters does an actor at position
C at center stage have?
b. What angle of view of these characters does the orchestra conductor at
point D have?
c. What angle of view does an audience member at point E have?
1
2
} (80°) 5
°
Geometry
IDEA! Works
213
Lesson 10.2, continued
8. minor arc 9. minor arc 10. semicircle
Practice A
14. 708 15. 2908 16. 2808 17. 908 18. 2708
19. 1208 20. yes; Because the radii are >, the
circles are >, so because they have equal measure,
the arcs are >. 21. yes; The radii are >, so the
circles are >, and because 115 1 135 1 110 5
360, the arcs have equal measure, so they are >.
22. 308 23. minor arc 24. 8 25. 2108 26.
2408
Problem Solving Workshop:
Worked Out Example
1. m∠1 5 868 2. m∠1 5 1168, m∠ 2 5 648
3. m(arc 1) 5 1648, m(arc 2) 5 1968
4. m∠1 5 828, m∠ 2 5 988
5. m(arc 1) 5 538, m∠ 2 5 1338
6. m(arc 1) 5 1028, m(arc 2) 5 408
7.m(arc 1) 5 908, m∠ 2 5 908
8. m∠1 5 24.58 9. m∠1 5 368
10. m(arc 1) 5 558, m∠ 2 5 37.58 11. 168
12. 35 13. 7 14. 135 15. a. 808 b. 408 c. 218
1. a. 368 b. 1588 c. 2028 d. 1728
Problem Solving Workshop:
Mixed Problem Solving
Lesson 10.3
Practice A
1. 9 2. 6 3. 8 4. 1058 5. 858 6. 1308
7. yes 8. no; A diameter that is perpendicu}
lar to a chord bisects the chord, but QS does not
}
bisect chord PR. 9. 10 10. 558 11. 1198
12. yes 13. no 14. 7 15. 7
16. 3 17. 7 18. Measure the chord length
across the top of the heads side from the “L” to the
“Y” in LIBERTY and the chord length across the
tails side from the “Q” to the last “R.” in QUARTER DOLLAR. If the chord lengths are the same,
then the arcs are the same.
Quiz 1
}
}
1. a. 40 ft b. 58 ft 2. a. 468 b. 468, 1348, 1348
c. 628 3. 5 4. a. 308 b. 1508
Quiz 2
1. x 5 85, y 5 100, z 5 160
2. x 5 75, y 5 85, z 5 210
3. 38 4. 143 5. 114 6. 130
Lesson 10.6
Practice A
1. 3, 9; 15 2. 4, x; 8 3. x, 18; 22.5
4. x, 12; 16 5. 16; 8 6. 18; 6
7. 12 8. 4 9. 12.5
}
1. Yes, 242 1 102 5 262; BC ⊥ AB
}
2. No, 52 1 112 Þ 122; AC is not ⊥ AB
3. 1008 4. 808 5. 2608 6. 1808 7. 3 8. 7
10. 7.4 11. 9 12. 9 13. 5.7 14. 7.7
15. 3 16. 28.1
Lesson 10.4
17. a. 50 cm b. 80 cm, 80 cm c. 128 cm
d. 178 cm e. 89 cm
Practice A
Lesson 10.7
1. 798 2. 128 3. 808 4. 1808 5. 168 6. 528
7. 348 8. 628 9. 1128 10. 628
11. ∠ C > ∠ D, ∠ E > ∠ F
12. ∠ W > ∠ Z, ∠ X > ∠Y 13. no; The 708 and
1308 angles are not supplementary. 14. yes
15. x 5 118, y 5 118 16. x 5 112, y 5 76
17. x 5 105, y 5 75 18. x 5 91.5, y 5 106
19. m∠ A 5 408, m∠ C 5 328
20. m∠ A 5 738, m∠ C 5 318
A24
Lesson 10.5
Geometry
IDEA! Works
Practice A
1. C 2. F 3. A 4. B 5. E 6. D 7. (0, 0); 5
8. (0, 4); 3 9. (5, 0); 4 10. (2, 4); 4
11. x 2 1 y 2 5 36 12. x 2 1 ( y 2 2)2 5 4
13. (x 1 2)2 1 y 2 5 16 14. x 2 1 y 2 5 4
15. (x 2 2)2 1 y 2 5 9
16. (x 2 5)2 1 ( y 1 6)2 5 1
17. (x 1 3)2 1 ( y 2 7)2 5 36
18. x 2 1 y 2 5 49 19. (x 1 1)2 1 (y 2 2)2 5 25
Copyright © Holt McDougal Math. All rights reserved.
ANSWERS
11. minor arc 12. 708 13. 1808