This is a special case of the "circumcenter of mass" theorem. See the [Wikipedia article][1] and

Akopyan, Arseniy V., Some remarks on the circumcenter of mass, Discrete Comput. Geom. 51, No. 4, 837-841 (2014). ZBL1301.51022. [1]: https://en.wikipedia.org/wiki/Circumcenter_of_mass

This is a special case of the "circumcenter of mass" theorem. See the Wikipedia article and

Akopyan, Arseniy V., Some remarks on the circumcenter of mass, Discrete Comput. Geom. 51, No. 4, 837-841 (2014). ZBL1301.51022.