5.2.1.3 Transformations on the plane

Problem: Inside the triangle \( A B C \) an arbitrary point \( M \) is chosen. Find the perimeter of the triangle with vertices at the centroids of the triangles \( A B M, B C M \) and \( A C M \), if the perimeter of the triangle \( A B C \) is equal to \( 2 p \).