Let A', B', C' be the altitude feet; Ab, Ac the reflections of A' on BB', CC'; Oa the reflection of the circumcenter O on the side BC; Ga the centroid of OaAbAc. Define analogously Gb, Gc. The triangles ABC, GaGbGc are perspective with center X, and orthologic with centers Y, Z. The three points X, Y, Z lie in the Euler line.