Each side of [math]\bigtriangleup{ABC}[/math] is tangent to circle [math]O[/math] at the points [math]D[/math], [math]E[/math], and [math]F[/math]. Find the perimeter of [math]\bigtriangleup{ABC}[/math].
[list=1] [*]Identify the lengths of each side of the triangle. [*]Calculate the perimeter of [math]\bigtriangleup{ABC}[/math]. [/list]