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Quizzes

Circles: Circular Logic Quiz

Think you’ve got your head wrapped around Circles? Put your knowledge to the test. Good luck — the Stickman is counting on you!
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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?


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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?


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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 = 144
Q. 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
542 units
8 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?


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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
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