Circles

SAT Math· difficulty 4/5

From external point P, two secants are drawn to a circle. The first secant has total length 10 with external segment 4. The second secant has external segment 5. What is the total length of the second secant?

  • A

    8

    check_circle
  • B

    10

  • C

    6

  • D

    12

Explanation

By secant-secant: (textwhole1)(textext1)=(textwhole2)(textext2)(\\text{whole}_1)(\\text{ext}_1) = (\\text{whole}_2)(\\text{ext}_2). So 10(4)=L(5)10(4) = L(5), giving L=8L = 8.

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