Circles
Date:
Name:
1.
What is the approximate area of a 70 sector of a circle with a
radius of 8 inches?
2.
Crops are often grown using a technique called center pivot
irrigation that results in circular shaped elds.
4.
Use the diagram to answer the question.
Here is a satellite image taken over elds in Kansas that use this
type of irrigation system.
This circle, with center point Q, has a radius of 10 centimeters.
The length of the minor arc NP is 20.42 centimeters. To the
nearest degree, what is the value of x?
5.
An apple pie is cut into six equal slices as shown below.
If the irrigation pipe is 450 m in length, what is the area that
2
can be irrigated after a rotation of
radians?
3
If the diameter of the pie is ten inches, what is the approximate
arc length of one slice of pie?
6.
What is the length of AB if radius AD = 14?
(
3.
Line segments AB and CB intersect outside of circle P as shown
below.
What is the value of x?
page 1
7.
!
RB is tangent to a circle, whose center is A, at point B. BD is a
diameter.
11.
What is mO CBR?
8.
Points E, F, G, and H are points of tangency. The length of AB
is 10 cm. The length of DC is 20 cm. What is the length, in
cm, of BC ?
Find the unknown length in the picture below.
12.
9.
A certain machine is to contain two wheels, one of radius
3 centimeters and one of radius 5 centimeters, whose centers are
attached to points 14 centimeters apart. The manufacturer of this
machine needs to produce a belt that will t snugly around the
two wheels, as shown in the diagram below. How long should
the belt be?
Quadrilateral ABCD is inscribed in a circle as shown in the
diagram below.
If mO A = 85 and mO D = 80 , what is mO B?
13.
10.
Circle J is inscribed in isosceles trapezoid ABCD, as shown
below.
Solve for x and y. What are the measures of the angles of the
quadrilateral?
!
AP is tangent to circle O at A, circle O has a radius of 6 ft,
circle P has a radius of 2 ft, and AB=6 ft.
What is CD?
page 2
Circles
14.
Use the gure to answer the following question.
18.
What is the approximate area of the shaded region?
19.
Circle E is shown below.
The endpoints of the chord of circle O are A and B, two vertices
of a triangle. The third vertex, C, can be located anywhere
along the dashed arc. If you locate the vertex so that it forms a
triangle that has the largest possible area, which of the following
must be true?
15.
A.
AB = BC = AC
B.
C.
AC > BC
D. AC = BC
AC < BC
Triangle ABC is inscribed in circle O as shown in the
below.
gure
What is the measure of O B?
16.
The measure of GHJ is (5x
50) .
The measure of KLF is (3x + 30) .
The radius of circle O shown below is 8 units. The area of the
shaded region is 41 the area of the circle.
What is the measure of O KEF?
20.
The point (3; 7) is a vertex of a triangle. When the triangle is
re ected over the y-axis, what are the coordinates of the image
of the vertex?
21.
Triangle ABC has vertices (1; 2), (5; 1), and ( 2; 0). Sarah
translated the triangle 2 units horizontally and 3 units vertically.
What are the vertices of the new triangle?
22.
What are the coordinates of the image of point P( 3; 7) after
a re ection about the line y = 2?
23.
Given the original point (x; y) choose the rule for the translation
“4 right, 3 down.”
What is the length of chord BC?
17.
Which of the following statements is true?
A.
A chord is contained in a tangent.
B.
A chord is contained in a radius.
C.
A chord is contained in a secant.
D. A chord is contained in an arc.
page 3
Circles
24.
The diagram below shows four points that form square ABCD.
28.
Right triangle PQR has sides of length 6 units, 8 units, and
10 units. The triangle is dilated by a scale factor of 4 about
point Q. What is the area of triangle P 0 Q 0 R 0 ?
29.
^ XYZ is dilated by a factor of 12 . What is the ratio of the area
of ^ XYZ to the area of its image, ^ X 0 Y 0 Z 0 ?
30.
Triangle LMN and triangle EFG are similar triangles.
Triangle EFG is shown on the grid below. If the coordinates of
point L are (4; 3) and the coordinates of point M are (4; 7), what
are the coordinates of point N?
31.
Which of the following transformations always preserves the
dimensions of a gure?
If square ABCD is transformed by the rule (x; y) ) (2x; 3y)
into the image A'B'C'D', what type of quadrilateral is image
A'B'C'D'?
25.
Given:
AB with coordinates of A( 3; 1) and B(2; 1)
A0 B0 with coordinates of A0 ( 1; 2) and B0 (4; 4)
Which translation was used?
26.
A.
(x; y) ! (x + 2; y + 3)
B.
C.
(x; y) ! (x
D. (x; y) ! (x
2; y + 3)
(x; y) ! (x + 2; y
2; y
3)
I.
3)
translation
II. rotation
III. re ection
Triangle PQR is shown.
IV. dilation
A.
I, II, and III
B.
I, II, and IV
C.
I, III, and IV
D. II, III, and IV
32.
Three transformations will be performed on triangle ABC. Which
set of transformations will always produce a congruent triangle?
33.
A pentagon has a perimeter of 40 cm. What is the perimeter of
the pentagon after a translation of (x; y) ! (x 7; y + 5) and a
rotation of 90 clockwise about the origin is applied? How do
you know?
34.
What is the area of the shaded sector?
What are the coordinates of P0 when ^ PQR is dilated by a
scale factor of 3 using the origin as the center?
27.
^ GHJ with vertices G( 2; 4), H(3; 6),and J(3; 2) is dilated
by a factor of 31 . What are the coordinates of the vertex of the
image ^ G0 H 0 J 0 that lies in the second quadrant?
page 4
Circles