Question

Please help me find X

Answer 1

Answer:

  x = 2

Step-by-step explanation:

The product of distances from the intersection of secants to the near and far intersections with the circle are the same. For a tangent, the near and far points of intersection with the circle are the same. This relation tells us ...

  (2√3)(2√3) = x(x +4)

  12 = x² +4x

  16 = x² +4x +4 . . . . . add the square of half the x-coefficient to complete the square

  4² = (x +2)² . . . . . . . . write as squares

  4 = x +2 . . . . . . . . . . positive square root

  2 = x . . . . . . . . . . . . . subtract 2

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Alternate solution

If you believe x to be an integer, you can look for factors of 12 that differ by 4.

  12 = 1×12 = 2×6 = 3×4

The factors 2 and 6 differ by 4, so x=2 and x+4=6.