Note that a chord will be bisected into two equal segments by a line passes thru the center of the circle and perpendicular to the chord.
The two segments are :
3x - 2 and x + 8
Equate both segments.
[tex]\begin{gathered} 3x-2=x+8 \\ 3x-x=8+2 \\ 2x=10 \\ x=\frac{10}{2}=5 \end{gathered}[/tex]
The value of x is x = 5
Substitute x = 5 to any of the segment and multiply is by 2.
[tex]\begin{gathered} 2\times(3x-2)=2\times(3\times5-2) \\ \Rightarrow2\times(13)=26 \end{gathered}[/tex]
The answer is HG = 26
