Circles

SAT Math· difficulty 3/5

A chord of a circle is perpendicular to a diameter and is bisected by it. If the radius is 10 and the chord is 12 from the center... actually, the chord has length 16 and the radius is 10. What is the distance from the center to the chord?

  • A

    36\sqrt{36}

  • B

    6

    check_circle
  • C

    8

  • D

    10

Explanation

The perpendicular from the center bisects the chord, forming a right triangle: half-chord = 8, radius = 10. Distance d=sqrt10282=sqrt36=6d = \\sqrt{10^2 - 8^2} = \\sqrt{36} = 6.

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