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 P in Af; let A1 = reflection of A* in A; define B1 and C1 cyclically. Then A1B1C1 is an equilateral triangle homothetic to the outer (inner) Napoleon equilateral triangle, with homothetic center H1.
Dao Thanh Oai, June 29, 2022
