Can you prove the claim given below? Inspired by [Lester's theorem][1] I have formulated the following claim:

>**Claim.** Given any scalene triangle $\triangle ABC$ . Let $D$ be the reflection of incenter in sideline $AB$, and define $E$ and $F$ cyclically. The lines $CD$, $BF$, $AE$ concur in [X(79)][2] . Then, the two Fermat points , incenter and $X(79)$ lie on the same circle.

[![enter image description here][3]][3]

GeoGebra applet that demonstrates this claim can be found [here][4].


  [1]: https://en.wikipedia.org/wiki/Lester%27s_theorem
  [2]: https://faculty.evansville.edu/ck6/encyclopedia/ETC.html
  [3]: https://i.sstatic.net/jgnBL.png
  [4]: https://www.geogebra.org/m/r63eeexm