Circles Practice

Sample questions

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1. Sample 1difficulty 2/5

   What is the radius of the circle with equation $(x-2)^2 + (y-7)^2 = 49$?

   • A

     7

     check_circle
   • B

     14

   • C

     49

   • D

     $\sqrt{7}$

   Why

   In standard form $(x-h)^2 + (y-k)^2 = r^2$, we have $r^2 = 49$, so $r = 7$.

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2. Sample 2difficulty 2/5

   A circle has diameter 10. What is its circumference?

   • A

     $20\pi$

   • B

     $5\pi$

   • C

     $25\pi$

   • D

     $10\pi$

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   Why

   Circumference $= \\pi d = \\pi(10) = 10\\pi$.

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3. Sample 3difficulty 2/5

   A circle has radius 7. What is its circumference?

   • A

     $28\pi$

   • B

     $14\pi$

     check_circle
   • C

     $49\pi$

   • D

     $7\pi$

   Why

   Circumference $= 2\\pi r = 2\\pi(7) = 14\\pi$.

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4. Sample 4difficulty 2/5

   What is the center of the circle with equation $(x-3)^2 + (y+5)^2 = 16$?

   • A

     $(3, -5)$

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   • B

     $(-3, 5)$

   • C

     $(-3, -5)$

   • D

     $(3, 5)$

   Why

   The standard form is $(x-h)^2 + (y-k)^2 = r^2$ where $(h,k)$ is the center. Here $h=3$, $k=-5$, so the center is $(3, -5)$.

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5. Sample 5difficulty 2/5

   A circle has radius 6. What is its area?

   • A

     $36\pi$

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   • B

     $72\pi$

   • C

     $12\pi$

   • D

     $6\pi$

   Why

   Area $= \\pi r^2 = \\pi(6)^2 = 36\\pi$.

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