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 P in A;
let A2 = reflection of A* in Af. Define B2 and C2 cyclically. Then A2B2C2 is an equilateral triangle homothetic with the outer (inner) Napoleon equilateral triangle, with homothetic center H2.
Dao Thanh Oai, June 29, 2022
