Minimal inradius of an arbitrary convex quadrilateral

How does one compute the minimal inradius of an arbitrary convex (not necessarily tangential) quadrilateral? Is there an easy formula I did overlook? Or is embedding the convex into a tangential quadrilateral the easiest approach?

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There is no minimal inradius of an arbitrary convex quadrilateral, since the inradius can be as small as you like but not $0$. Perhaps you forgot to state some condition like the area or perimeter of the quadrilateral? – joriki Jul 22 '12 at 12:53
What do you mean by "minimal inradius of a convex quadrilateral"? – Christian Blatter Jul 22 '12 at 13:54
Perhaps you meant either the minimum circumradius or the maximal inradius? – Joseph O'Rourke Jul 22 '12 at 14:49
Indeed minimal was a misnomer. I mean the radius of a circle fully enclosed by the quadrilateral, yet touching as many as possible edges. If there is more than one possibility touching three edges, choose the minimal. – litro Jul 22 '12 at 19:42