Answer:
x = 9
Explanation:
Formula
The secant and tangent lines bear the following relationship
(tangent line )^2 = the outside secant line * length of the whole line
Givens
tangent line = 15
outside secant line = x
length of whole secant line = x + 16
Solution
15^2 = x ( x + 16)
15^2 = x^2 + 16x
225 = x^2 + 16x
x^2 + 16x - 225 = 0
Answer and Discussion
The equation has two factors.
(x - 9)(x + 25) =0
x + 25 has no meaning. There cannot be a negative length in this level of geometry.
The answer is x - 9 = 0
x = 9