Answer:
12. x = 5
13. z = 2√21
Explanation:
For any given pair of intersecting secants, the product of the distances to the near and far circle intersections is a constant. When those intersection points are both the same (as for a tangent), the same is still true: the product is the square of the length of the tangent segment.
12. (x-2)((x-2) +(x+4)) = 4(4+5)
(x -2)(2x +2) = 36
x^2 -x -2 = 18 . . . . . . . divide by 2 and eliminate parentheses
(x -5)(x +4) = 0 . . . . . . subtract 18 and factor
x = 5 . . . . . . . . . . . . . . by the zero product rule, the only solution with x > 2
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13. 6(6+8) = z^2
z = √84 . . . . . . . . take the square root
z = 2√21 . . . . . . . simplify