In this question we have to use the formula that relates the lengths of secant and tangent .
And according to the theorem, the square of tangent is equal to the product of length of the part of secant that is outside the circle and total length .
And according to the formula, we will get
[tex] x^2 = 4(4+16) [/tex]
[tex] x^2 = 4*20 [/tex]
[tex] x^2 = 80 [/tex]
Taking square root to both sides
[tex] x = \sqrt{80} = 4 \sqrt 5 = 8.9 . [/tex]
So for the given diagram, and with the given values, the value of x is 8.9
