Find X using the image.

9514 1404 393

  x = 2

Step-by-step explanation:

The square of the tangent is equal to the product of the secant lengths to the near and far circle intersections.

  (x +4)² = (2x -1)(2x -1 +9)

  0 = (2x -1)(2x +8) -(x +4)² = (4x² +14x -8) -(x² +8x +16)

  0 = 3x² +6x -24 = 3(x² +2x -8) = 3(x +4)(x -2)

This has solutions x = -4 and x = 2. Only the latter works in this geometry.

  x = 2

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