Concyclic Points in Inscriptible Quadrilateral
What Might This Be About?
In a convex inscriptible quadrilateral $ABCD,$ the perpendicular bisectors of the sides form another inscriptible quadrilateral - $EFGH.$ Let $I$ be the incenter of that quadrilateral.
Then the incenters of triangles $IAB,$ $IBC,$ $ICD,$ $IDA$ are concyclic.
The fact that $EFGH$ is inscriptible is proved elsewhere. It was discovered by Michael be Villiers several years ago.
Proof of the concyclicity of the incenters is wanting.
The problem has been posted by Dao Thanh Oai (Vietnam) at the CutTheKnotMath facebook page.