# How to determine the intersection of 6 planes?

ABCD is a tetrahedron (not necessarly a regular one). A Monge's plane is a plane which is perpendicular to an edge and goes through the middle of the opposite edge.

I want to prove that the 6 Monge's planes of this triangle converge in a unique point and I haven't got any idea of the way to do this.

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You've tried taking the coordinate geometry route? – J. M. Oct 26 '11 at 15:02
I tried but there are too many unknowns and I don't see how to characterize this kind of conditions. – Skydreamer Oct 26 '11 at 15:11
The strategy I had in mind was for you to take three of those planes, find their intersection, and then verify that that point lies in those three other planes... – J. M. Oct 26 '11 at 15:15
Okay, this might help you with simplifying things: position your tetrahedron such that one vertex is at the origin and one of the edges lies on an axis. Have one of the faces lie in a coordinate plane, if needed. You might want to use the formulae here to help you with assembling plane equations. – J. M. Oct 26 '11 at 15:29