Question

Angle measures and segment lengths. Please help

Answer 1

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.

$\Rightarrow x^2 = 24\times 10$

$\Rightarrow x^2 = 240$

Taking square root on both sides.

$\Rightarrow x = 4\sqrt{15}$

$\Rightarrow x = 15.5$

The length of the tangent segment is 15.5 in.