Question

find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale

Answer 1

14.39

Explanation:

Theorem 12-15 III

(y+z) y=t squared

(9+14)9=x squared

23•9=x squared

207 =x squared

Square root of 207 is 14.39

Answer 2

14.4

Explanation:

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

_____

Additional note on the geometry

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