Let ABC be a triangle with centroid G and outer-Fermat (or inner-Fermat) triangle AfBfCf. P be arbitrary point in the plane. Let A* = reflection of Af in P; let A4 = midpoint of A*A. Define B4 and C4 cyclically. Then A4B4C4 is an equilateral homothetic to the outer (inner) Napoleon equilateral triangle, with homothetic center H4.
Dao Thanh Oai, June 29, 2022
