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Circles

SAT Math· difficulty 5/5

Two circles have equations (x−1)2+(y−2)2=9(x-1)^2 + (y-2)^2 = 9 and (x−7)2+(y−10)2=16(x-7)^2 + (y-10)^2 = 16. What is the distance between their centers?

  • A

    All of the above

    check_circle
  • B

    100\sqrt{100}

  • C

    36+64\sqrt{36+64}

  • D

    10

Explanation

Centers are (1,2)(1, 2) and (7,10)(7, 10). Distance =sqrt(7−1)2+(10−2)2=sqrt36+64=sqrt100=10= \\sqrt{(7-1)^2 + (10-2)^2} = \\sqrt{36+64} = \\sqrt{100} = 10. All three expressions equal 10.

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