1 CIRCLES: HOMEWORKS
Chris Delany
HW 1: Lesson I: Introduction to Circles
( A word bank will be provided, since the students haven’t been exposed to all these words ie compass)
Solution:
2 HW 2: Lesson II: Arcs, Chords, Tangents
Display your understanding of 5 of the following by the use of pictures, diagrams, and/or proofs:
-Congruent Arcs, Arc Addition Postulate, The 3 Arc Theorems, Important Properties of Chords, Tangent Postulate,
The 2 Tangent Theorems, Common Tangents
HW 3: Lesson III: Discovering Pi
Continue investing pi online. Find one interesting pi fact, and we will share them as a class tomorrow. For example,
you can read about the world record holder for the most digits of pi memorized. Write down your pi facts in your
math journal.
http://www.pi-world-ranking-list.com/lists/details/luchaointerview.html
HW 4: Lesson IV: Measuring Circles
Convert each degree measure to exact radian measure.
1. -415
2. -519
3. 570
4. -174
5. 473
6. 905
Convert each radian measure to degree measure.
1.
29
2.
55
36
3.
12
36
4.
17
5.
5
18
8
9
6.
53
36
Arc Length/ Sector Area
1.
Find the length of arc DE and the area of sector DGE. Also find the area of the segment outside of equil.
triangle DGE.
3 2.
If the length of arc GH is 2*pi and the circumference of the circle is 3*pi, find the central angle.
HW 5: Lesson V: Using a Compass
Write about the process of how to use a compass in your math journal. What did you learn from today’s activities?
How could you use a compass in a real-world application? What would be another tool that could be used to draw
circles?
HW 6: Lesson VI: Standard Form, Graphing Circles
Write the standard form of the equation of the circle with the given radius and center.
1.
1
2.
C (0,0); r =
22
3.
C (-8, -9); r =
3
34
C (-2, -5); r =
5
11
Write the standard equation, the center, and the radius for each circle. 1. x2 + y2 = 49 2. x2 + y2 = 1/16
3. x2 + y2 + 6y + 1 = 0
Write the standard equation for each circle.
1.
2.
3.
4 Match the equation of the circle with its graph. 121
(x - 1)2 + (y + 4)2 = 16
B. (x - 2)2 + y2 =
1
C. (x - 3)2 + (y + 2)2 =
4
1.
2.
4
3.
HW 7: Lesson VII: Circumscribed Polygons and Inscribed Angles
Choose:
1.
59
Given the labeled diagram at the
left, with diameter
.
44
43
Find x.
34
Choose:
2.
Given circle with center
indicated.
Find x.
55
70
110
290
5 Choose:
3.
Given circle with center
indicated.
Find x.
36
54
90
108
Choose:
4.
Given diameter.
Find x.
28
56
62
124
Choose:
5.
Given circle with center
indicated.
Find x.
25
50
100
125
Choose:
6.
Given circle with center
indicated and
24
48
72
Find x.
96
6 Choose:
7..
45
Given diameter
60
Find x.
90
180
Choose:
8.
Given circle with
center indicated and
inscribed
quadrilateral.
Find x and y
x = 75, y = 94
x = 94, y = 75
x = 86, y = 105
x = 105, y = 86
Choose:
9.
Given circle with center
indicated.
x = 100
Find x.
x = 50
x = 80
x = 40
Choose:
10.
x = 37
Given diameter
Find x.
x = 53
x = 74
x = 90
7 CIRCLES: FINAL ASSESSMENT
Here is the final assessment for all the material you have learned in this lesson. If you have time after you finish,
review your answers. Good luck!
For 1-4, find the circumference. Use 3.14 for .
1.
2.
NY = 43 ft
NB = 66 in
3. radius = 27 in
4. diameter = 40 cm
5. Draw a circle and inscribe an obtuse
triangle in the circle.
6. What is the name of the longest chord in
any circle?
7. Can any chord on a circle be a radius?
8. Describe the three possible arcs that could
be found on a circle.
9. What is true of all radii of a circle?
10. How many chords on a circle can be a
diameter of the circle?
11. What is a semicircle?
12. Define a circle without using the word
"round".
13. What is an inscribed polygon?
14. If an arc makes a central angle of 109°, is
it a major or minor arc? Explain how you
know.
15. Draw a circle O with radius 22. Then
16. An isosceles right triangle inscribed in a
circle. If the length of the two equal sides
draw radii
and
to form an angle
is 22 cm, find the radius of the circle.
of 60degrees. What is the length of
?
17. Circles that have same radius are called
______.
semicircles
conjoint circles
concentric circles
congruent circles
18. A ______ is a line that intersects a given
circle in two points.
tangent
chord
secant
diameter
8 19. What is wrong with the statement: "All
radii are congruent."?
20. Jennifer is working on a sewing project.
She has a circular piece of fabric, and
needs to find the center. How can she do
that?
21. How can you illustrate the definition of a
circle?
22. Can any chord of a circle ever equal the
radius?
23. In the figure, the radius for P is r and
the radius for Q is R. Which of the
following statement is true?
24. Given circle O with segment AB tangent
to the circle at A. If OA = AB, what kind
of triangle is OAB?
Circles P and Q have two common
tangents.
PQ = R - r
PQ = R + r
Circles P and Q have four common
tangents.
25. The radius of the inscribed circle is 3. If
the length of the hypotenuse of the right
triangle ABC is 20, what is the perimeter
of the triangle?
a scalene triangle
an isosceles right triangle
an equilateral triangle
an equilateral acute triangle
an isosceles obtuse triangle
26.
and
are tangents to circle O.
If OA = 30 cm, OP = 15 cm, and
m PAQ = 60 , find the area of
quadrilateral OPAQ.
9 27.
,
, and
are tangents to circle
O. If PA = 23, find the perimeter of
triangle PRS.
28. If OM = 5 and AB = 20, what is the radius
of O?
29. Regular octagon ABCDEFGH is inscribed
in circle O. Diameter
is extended as
shown. Find (a) m
HJG (d) m K.
3.
Tangent
(b) m
ABF (c) m
intercepts circle O at B.
Chord
is drawn. If m
m CBD.
4.
= 58 , find
31. Congruent inscribed angles always
intercept congruent arcs.
False
True
30. A, B, C, D, E, and F are points on a circle.
If m AEC = 73 and m ECD = 40 ,
what is the value of y - x?
In circle O, diameter
, radius
chord
are all drawn. If m
, find m OCB.
32.
In circle O, chords
and
, and
AOC = 50
intersect
at E. m
= 63 and m CEB = 83 .
Find the sum of the measures
of
and
.
10 34.
Tangents
and
are drawn to
circle O. If the measure of
major
is 242 , find m
35. How is it possible for a huge circle and a
tiny circle to each have the same number
of degrees?
C.
36. What is the relationship between a central 37.
In circle O, secant
and
angle and an angle inscribed in the same
chord
intersect. If m
= 186 and
arc?
m
= 47 , find m
CBD.
38. There is no rule for an angle formed by a
secant and a chord. How do you find its
measure?
39. The measure of a minor arc is defined to
be the measure of its ______.
40. A ______ is a line that intersects a given
circle in two points.
41. A triangle inscribed in a semicircle is
______.
chord
tangent
diameter
secant
42. How many common tangents can be
drawn to the two circles?
an equilateral triangle
an acute triangle
a right triangle
an obtuse triangle
43.
P and Q have radii 9 and 11. Given
the distance between the center of the
circles P and Q is 10, find the length of
the common chord
.
In circle O, chords
and
0
3
4
1
2
44. Amber is working on a sewing project.
She has a circular piece of fabric, and
needs to find the center. How can she do
that?
45.
intersect
at E. If m
= (7x - 117) , m
= (4x
- 92) , and m CEB = 114 , find the
value of x
11 46.
P and Q are congruent circles that
intersect at C and D. What kind of
quadrilateral must PCQD be?
a square
a parallelogram
a rhombus
a trapezoid
47. Explain the difference between a line
segment containing the center of a circle
with endpoints on the circle and a line
segment that has one end point on the
circle and another at its center.
For 48-50, write the standard form and general form for each circle.
48.
49.
50.
Additional Problem: Construct a circle through a given 3 points using what you have learned about compasses.