Setup the geometric relationship

Draw a perpendicular from the center to the chord, which bisects the chord. This forms a right-angled triangle with the radius as the hypotenuse, the distance as one leg, and half the chord as the other leg.

$R^2 = d^2 + x^2$

Substitute the given values

Substitute $R = 17$ and $d = 8$ into the equation to find the half-chord length $x$.

$17^2 = 8^2 + x^2 \implies 289 = 64 + x^2$

Solve for half-chord length

Isolate $x^2$ and calculate the square root to find the length of the segment.

$x^2 = 289 - 64 = 225 \implies x = \sqrt{225} = 15$

Calculate the full chord length

Since the perpendicular from the center bisects the chord, the total length of the chord $AB$ is $2x$.

$AB = 2 \times 15 = 30$