Question

Find the measure of the line segment GE. Assume that lines which appear tangent are tangent.

Answer 1

The measure of the line segment GE is
`18\ units`

Explanation:

we know that

The Intersecting Secant-Tangent Theorem states that, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

so

In this problem

`GE*GF=GH^(2)`

substitute the values

`(8+x)(8)=12^(2)`

solve for x

`8x+64=144`

`8x=144-64`

`8x=80`

`x=10`

Find the measure of the line segment GE

`GE=8+10=18\ units`