Given:
m is the bisector of AB
In a triangle ADC,
[tex]DC^2=(6x-25)^2-83^2\ldots\text{ (1)}[/tex]
In a triangle BDC
[tex]DC^2=(3x+77)^2-83^2\ldots\text{ (2)}[/tex]
From equation(1) and (2),
[tex]\begin{gathered} (6x-25)^2-83^2=(3x+77)^2-83^2 \\ 6x-25=3x+77 \\ 3x=77+25 \\ 3x=102 \\ x=34 \end{gathered}[/tex]
