The value of x is 9.
To solve for x using the secant segments from external points theorem, we need to use the following equation:
EX * EY = AX * AY
where:
EX is the length of the external secant segment from point E to the circle,
EY is the length of the external secant segment from point E to the circle,
AX is the length of the secant segment from point A to the circle, and
AY is the length of the secant segment from point A to the circle.
In this case, we are given that:
EX = 7
EY = 8
AX = x
AY = 6
Substituting these values into the equation, we get:
7 * 8 = x * 6
56 = 6x
x = 56 / 6
x = 9
Therefore, the value of x is 9.