Answer:
The measure of the line segment GE is [tex]18\ units[/tex]
Step-by-step 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
[tex]GE*GF=GH^{2}[/tex]
substitute the values
[tex](8+x)(8)=12^{2}[/tex]
solve for x
[tex]8x+64=144[/tex]
[tex]8x=144-64[/tex]
[tex]8x=80[/tex]
[tex]x=10[/tex]
Find the measure of the line segment GE
[tex]GE=8+10=18\ units[/tex]
