The triangle Δ N_1 N_2 N_3 formed by joining a set of three Neuberg centers (i.e., centers of the Neuberg circles) obtained from the edges of a given triangle Δ A_1 A_2 A_3. Similarly, a second set of three Neuberg circles with centers N_1^, , N_2^, , and N_3^, can be obtained from the main circles by reflection in their respective sides of the triangle, producing the second Neuberg triangle Δ N_1^, N_2^, N_3^, .