Don't use arc much myself. As i understand it you can't change the way it works - pick the 2 ends then drag out the radius.
having dragged out an approximate radius you can then type in an exact value and the arc will change to have that radius.
If you want to fillet a corner with say 10 radius, draw an arc of any size with tangents to the edges (the points where the arc goes purple), then having drawn it type 10r and hit enter. The arc will resize to 10 radius.
edit - corrected dud info thanks to DaveR's post below
The default entry for the Arc tool is the bulge or height above the arc's chord. If you want to define the arc's radius instead, append the value with the letter 'r'. So for a 30mm radius (assuming your default units are millimeters) you would type 30r followed by the Enter key.