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Quadrilateral and Radius Query (Posted on 2016-09-15) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts hand waving answer Comment 1 of 1
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.  

But GH is only 5.  So the radius can't even be as large as 2.5

Geometers Sketchpad gives the greatest R as about 2.105 when angle EFG is about 120.496

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