37-Another four incenter lie on a circles

Mr Tony Gacia share me the link:

A conjecture of Christopher Bradley

I inspired and construct and found some problems following:

Let  be a tangential quadrilateral.  are intersecton of perpendicular bisector of four sideline (show in thefigure). 

1- Prove that  are tangential quadrilateral.(Well-Known)

2- Four incircle of four triangles  are cyclic quadrilateral.

3-Deno  is center of incribed circle of quadrilateral , then four incenter of four triangles  lie on a circle.