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# Circles

# Circles: Circular Logic Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Circles**Q. Given one line and one circle that you can arrange in any way you like, what is the minimum number of points where they intersect?

0

1

2

3

4

Q. Given one line and one circle that you can arrange in any way you like, what is the maximum number of points where they intersect?

0

1

2

3

4

Q. Suppose line

*q*is tangent to ⊙*O*at the point*P*. Which of the following must be true?Line

*q*is parallel to*OP*and is not parallel to any other radius of ⊙*O*.Line

*q*is perpendicular to*OP*and is not perpendicular to any other radius of ⊙*O*.Line

*q*is parallel to*OP*and may be parallel to another radius of ⊙*O*.Line

*q*is perpendicular to*OP*and may be perpendicular to another radius of ⊙*O*.None of the above

Q. In the figure below, segments

*AC*and*BC*are tangent to ⊙*O*at points*A*and*B*, respectively. If*AO*= 3 cm and*AC*= 5 cm, what is*CB*?

3 cm

5 cm

6 cm

cm

There is not enough information to find

*CB*Q. What is the equation of a circle with radius 12 units and center at (3, -2)?

(

*x*– 3)^{2}+ (*y*+ 2)^{2}= 12(

*x*+ 3)^{2}+ (*y*– 2)^{2}= 12(

*x*+ 3)^{2}– (*y*– 2)^{2}= 12(

*x*– 3)^{2}+ (*y*+ 2)^{2}= 144(

*x*+ 3)^{2}+ (*y*– 2)^{2}= 144Q. What is the center of the circle with equation (

*x*– 5)^{2}– (*y*+ 18)^{2}= 67?(5, -18)

(5, 18)

(-5, -18)

(-5, 18)

No such circle exists

Q. What is the radius of the circle with equation (

*x*– 8)^{2}+ (*y*+ 1)^{2}= 54? units

54 units

54

^{2}units8 units

No such circle exists

Q. What is the exact circumference of the circle with equation (

*x*+ 5)^{2}+ (*y*+ 2)^{2}= 36?4π units

10π units

12π units

14π units

There is not enough information

Q. If line

*m*is tangent to ⊙*O*at*P*and the slope of the line containing*OP*is , what is the slope of line*m*?0

Q. Consider the circle with radius 6 units, centered at the origin. Where is the point (-3, 4) in relation to the circle?

In the interior of the circle

In the exterior of the circle

On the circle

Tangent to the circle

Perpendicular to the circle