Question

Find the value of x. X + 11 X-1 B 8 10 E x=

Answer 1

9514 1404 393

Answer:

  x = 7

Step-by-step explanation:

The product of secant lengths to the two intersection points is the same for both secants.

  (AD)(AE) = (AB)(AC)

  8(8+10) = (x-1)(x-1 +x+11)

  144 = 2x^2 +8x -10

  x^2 +4x -77 = 0

  (x +11)(x -7) = 0

Solutions to this quadratic are x = -11, x = 7. (These values make the factors zero.) Only the positive solution is useful here

  x = 7