In a convex quadrilateral EFGH, it is known that
EF = 3, FG= 6, GH = 5 and, HE = 8
Circle O - having radius R - is contained within quadrilateral EFGH.

Can R be greater than or equal to 3?
If so, provide an example.
If not, prove it.

It's clear from a bit of sketching that the largest circle will be tangent to the largest 3 sides.  FG and HE will be furthest apart where they meet GH.  

Posted by Jer on 2016-09-18 18:00:34