Circles

SAT Math· difficulty 3/5

From an external point P, a tangent to a circle touches the circle at point T. If PT = 12 and the distance from P to the center is 13, what is the radius of the circle?

  • A

    12

  • B

    1

  • C

    5

    check_circle
  • D

    313\sqrt{313}

Explanation

The radius perp\\perp tangent at T, forming a right triangle with hypotenuse PO = 13 and leg PT = 12. Radius =sqrt132122=sqrt25=5= \\sqrt{13^2 - 12^2} = \\sqrt{25} = 5.

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