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?
Minimal inradius of an arbitrary convex quadrilateral
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geometry
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0There 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? – 2012-07-22
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0What do you mean by "minimal inradius of a convex quadrilateral"? – 2012-07-22
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0Perhaps you meant either the minimum circumradius or the maximal inradius? – 2012-07-22
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0Indeed 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. – 2012-07-22