Let ABC be a triangle with centroid G and outer-Fermat (or inner-Fermat) triangle AfBfCf, and let P be an arbitrary point in the plane of ABC. Let A* = reflection of A in P; let A3 = midpoint of A*Af. Define B3 and C3 cyclically. Then A3B3C3 is an equilateral triangle homothetic to the outer (inner) Napoleon equilateral triangle,
with homothetic center H3.
Dao Thanh Oai, June 29, 2022
