Construct a circle inscribed in acute [math]\triangle ABC[/math].
[list=1] [*]Construct the angle bisectors of each angle. [*]Construct a perpendicular line from [math]D[/math] to each side. [*]Verify that the lengths of the perpendicular segments are equal. [*]Construct the inscribed circle with center [math]D[/math]. [/list]