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Circles: Chords, Tangents & Equations

Total questions: 20

Worksheet time: 2hrs 40mins

Name
Class
Date
1.


Fill in the blank:
Line m is tangent to circle C because it is _____________ to  CD\overline{CD}  at D.

a)

parallel

b)

perpendicular

c)

congruent

d)

touching exactly once

2.

If CE = 125 and CD = 44, Find DE.

(a)  

3.

Line AC  is tangent to Circle O at point C.
Find AC.

(a)  

4.

Line AC is tangent to Circle O at C.

Find AB.

(a)  

5.

If the radius of circle Q is 5 and PR = 12, Find PQ.

(a)  

6.

Find AC. (Do not include units.)

(a)  

7.

Find the radius of the circle. If necessary, round to the nearest tenth.

a)

11.4

b)

14

c)

18

d)

5.7

8.

Find RS.

a)

24

b)

12

c)

13

d)

26

9.

What is the center of the circle

x2+y24x+10y+13=0?x^2+y^2-4x+10y+13=0?  

a)

(2,5)

b)

(-2, 5)

c)

(2, -5)

d)

(-2,-5)

10.

Which of the following equations is the standard form of the circle

x2+y24x+10y+13=0?x^2+y^2-4x+10y+13=0?  

a)

(x2)2+(y+5)2=16(x-2)^2+(y+5)^2=16  

b)

(x2)2+(y5)2=16(x-2)^2+(y-5)^2=16  

c)

(x5)2+(y2)2=42(x-5)^2+(y-2)^2=42  

d)

(x+5)2+(y+2)2=42(x+5)^2+(y+2)^2=42  

11.

What is the center and radius of the circle

x2+y2=9?x^2+y^2=9?  

a)

(0,0); 3

b)

(0,3); 3

c)

(3,0); 3

d)

(3,3), 1

12.
Write the equation of a circle with center (h,k) and radius r.
a)
x2 + y2  = r2
b)
(x + h)2 +  (y + h)2 = r2
c)
(x - h)2 + (y - k)2 = r2
d)

(x - h)2 - (h - k)2 = r2

13.

What is the equation of the circle?

a)

(x+1)2 + (y +1)2 = 3

b)

(x+1)2 + (y -1)2 = 3

c)

(x+1)2 + (y +1)2 = 9

d)

(x-1)2 + (y -1)2 = 9

14.
What is the equation of this circle?
a)
(x + 3)2 + (y - 1)2 = 9
b)
(x - 3)2 + (y + 1)2 = 9
c)
(x - 3)2 + (y + 1)2 = 3
d)
(x + 3)2 + (y - 1)2 = 3
15.
Write the equation of a circle with center (7, 0) with radius 3. 
a)
(x - 7)2 + y2 = 9
b)
x2 + (y -7)2 = 9
c)
(x - 7)2 + y2 = 3
d)
x2 + (y -7)2 = 3
16.

Which graph corresponds to  (x-8)2 + (y+2)2 = 4

a)
A
b)
B
c)
C
d)
D
17.
In the equation (x+2)2+(y-3)2=4, the radius of the circle is...
a)
4
b)
2
c)
3
d)
16
18.

Point O is the center of each circle. Assume the lines that appear to be tangent are tangent. What is the value of the variable?

a)

8

b)

9

c)

15

d)

17

19.
What is the value of x?
a)
22
b)
25
c)
15
d)
20
20.

What is the definition of a tangent?

a)

A line that intersects the circle on two points.

b)

A line that passes through the center of the circle.

c)

A line segment that passes through the center of the circle.

d)

A line that intersects the circle on only one point.