Circles

SAT Math· difficulty 4/5

From external point P, a tangent of length 8 and a secant are drawn to a circle. The secant has external segment 4 (from P to the near intersection). What is the length of the entire secant from P?

  • A

    12

  • B

    16

    check_circle
  • C

    32

  • D

    8

Explanation

By the tangent-secant relationship: (texttangent)2=(textwholesecant)(textexternalsegment)(\\text{tangent})^2 = (\\text{whole secant})(\\text{external segment}). So 64=4L64 = 4L, giving L=16L = 16.

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