Let us analyze the diagram.
OB = OE
Since OB and OE are both perpendicular bisectors of AC and FD respectively, it follows that
AC = FD
Hence, we can equate the two values to solve for x.
[tex]-5x+13=4x-5[/tex]
Collecting like terms,
[tex]\begin{gathered} -5x-4x=-5-13 \\ -9x=-18 \\ x=2 \end{gathered}[/tex]
To find AC, we will put the value of x into the expression for AC.
Hence,
[tex]\begin{gathered} AC=-5x+13 \\ AC=-5(2)+13 \\ AC=-10+13 \\ AC=3 \end{gathered}[/tex]
Therefore, the value of AC is 3.
