Suppose that the lateral faces VAB, VBC and VCA of a triangular pyramid VABC all have the same height drawn from V. Let F be the point in plane ABC that is closest to V, so that VF is the altitude of the pyramid. Show that F is one of the special points of triangle ABC.

Pls find attached work.

Can i assume this is an equal lateral triangle?

If not i don't think i can get the altitude.