Angle measures and segment lengths. Please help

Given:

Secant segment = 14 in and 10 in

Length of tangent = x in

To find:

Length of tangent x.

Solution:

Secant segment = 14 in

External segment = 10 + 14

                             = 24 in

Tangent- secant theorem:

If a secant and a tangent intersect outside a circle, then the product of the secant segment and external segment is equal to the square of the tangent segment.

Taking square root on both sides.

The length of the tangent segment is 15.5 in.