Inscriptible Quadrilateral of Triangle Incenters

What Might This Be About?

24 January 2014, Created with GeoGebra

Problem

Given inscriptible quadrilateral $ABCD,$ construct four squares $AFGB,$ $BLXC,$ $CJKD,$ $DHIA$ (all either outer or inner, relative to the quadrilateral). Let $N,$ $M,$ $P,$ $Q$ be the incenters of triangles $BGL,$ $XCJ,$ $KDH,$ $IAF,$ respectively.

Inscriptible Quasrilateral of triangle incenters- problem

Then $MNPQ$ is an inscriptible quadrilateral.

Solution

Solution is wanting.

Acknowledgment

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

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