An arbitrary point M is taken on the basis of a regular triangular pyramid. Let K, L, N be the projections of M onto the lateral faces of this pyramid, and P be the intersection point of the medians of the triangle KLN. Prove that the straight line passing through the points M andP intersects the height of the pyramid (or its extension). Let us denote this intersection point by E. Find MP:PE if the dihedral angles at the base of the pyramid are equal to a. pyramidgeometry3D geometry