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Circles

SAT Math· difficulty 5/5

The points (2,5)(2, 5) and (8,5)(8, 5) lie on a circle. The center of the circle lies on the line y=2y = 2. What is the radius of the circle?

  • A

    34\sqrt{34}

  • B

    323\sqrt{2}

  • C

    18\sqrt{18}

    check_circle
  • D

    33

Explanation

The perpendicular bisector of the chord from (2,5)(2,5) to (8,5)(8,5) is x=5x = 5. Center is on x=5x=5 and y=2y=2: (5,2)(5,2). Radius =sqrt(5−2)2+(2−5)2=sqrt9+9=sqrt18=3sqrt2= \\sqrt{(5-2)^2 + (2-5)^2} = \\sqrt{9+9} = \\sqrt{18} = 3\\sqrt{2}. Note: sqrt18=3sqrt2\\sqrt{18} = 3\\sqrt{2}.

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