*Na, Nb, Nc* are [the outer Nagel points][1]. *A'B'C'* is the contact triangle. I claim that lines *A'B', A'C', B'C'* always [cut the sides of the triangle *NaNbNc* at six points][2] corresponding to an unknown circle.
 Surprisingly its center is not defined in the [ETC][3]:




[![unknown central circle][4]][4]

 Is it safe to say that this is actually the new [central circle][5] associated with the triangle *ABC*? 


  [1]: http://www.gogeometry.com/geometry/p684_triangle_nagel_point_excircle_incircle_tangency_point_concurrent.htm
  [2]: https://www.geogebra.org/geometry/juqugnam
  [3]: https://faculty.evansville.edu/ck6/encyclopedia/ETC.html
  [4]: https://i.sstatic.net/eT9Cf.png
  [5]: https://mathworld.wolfram.com/CentralCircle.html