Question

Find the value of x and the length of segment HG

Answer 1

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.

`\begin{gathered} 3x-2=x+8 \\ 3x-x=8+2 \\ 2x=10 \\ x=(10)/(2)=5 \end{gathered}`

The value of x is x = 5

Substitute x = 5 to any of the segment and multiply is by 2.

`\begin{gathered} 2*(3x-2)=2*(3*5-2) \\ \Rightarrow2*(13)=26 \end{gathered}`

The answer is HG = 26