# Concyclic Points in Inscriptible Quadrilateral

### What Might This Be About?

24 January 2014, Created with GeoGebra

### Problem

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.

### Solution

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.

### Acknowledgment

The problem has been posted by Dao Thanh Oai (Vietnam) at the CutTheKnotMath facebook page.

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