Napoleon Equilateral Triangles

Author:
Terry Tam
ABC is a triangle. For each side of ABC, there are 2 equilateral triangles (one outside and one inside) can be constructed. ABH and ABI are for the side AB, ACD and ACE are for the side AC, BCG and BCF are for the side BC. 3 centers of the "outside" equilateral triangles form another equilateral triangle JLN. 3 centers of the "inside" equilateral triangles form another equilateral triangle KMO.