The secant-secant product theorem states that if 2 secant segments are drawn to a circle from an external point, then the product of the length of one of the secants and its external portion is equal to the product of the length of the other secant and its external portion.
The length of the first secant in the image is x + 18, and the second is 24 + 16.
x + 18 times 18 = 40 times 16
18x + 324 = 640
18x = 316
x= approximately 17.6