27. Given a trihedral angle and a point $A$ on one of its edges. Points $B$ and $C$ slide along the other two edges. Find the geometric locus of the centroids of triangles $A B C$.
63.27. Answer. The part of the plane parallel to the face $B O C$ and at a distance of $d(A, B O C) / 3$ from it, lying inside the angle.