MathDB

Through a random point

C_1

from the edge

DC

of the regular tetrahedron

ABCD

is drawn a plane, parallel to the plane

ABC

. The plane constructed intersects the edges

DA

and

DB

at the points

A_1,B_1

respectively. Let the point

H

is the midpoint of the altitude through the vertex

D

of the tetrahedron

DA_1B_1C_1

and

M

is the center of gravity (barycenter) of the triangle

ABC_1

. Prove that the measure of the angle

HMC

doesn’t depend on the position of the point

C_1

. (Ivan Tonov)

Problem Statement