Find the value of x. if necessary, round your answer to the nearest tenth. the figure is not drawn to scale

14.4

This is a special case of the situation where two secant lines intersect a circle. The product of the near distance to the circle and the far distance to the circle from their point of intersection is a constant. A tangent is a degenerate case, where the near and far intersection points with the circle are the same point.

So, ...

... x · x = 9 · (9+14)

... x = 3√23 ≈ 14.4 . . . . . taking the square root

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Additional note on the geometry

This rule for the product of segments of secant lines also applies when the secants intersect inside the circle.