MathDB

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

and

P

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

Problem Statement