Thread: triangular pyramid

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.

If the perpendicular bisector of one side of a triangle meets a vertex of a triangle, it means that the two sides adjacent of that vertex are equal in length. If you have all three perpendicular bisectors meeting with the three opposite vertices, then the triangle is equilateral.

Otherwise, it's not.