Let a 1, a 2, a 3 denote the sides α1, α2, α3 the angles and A 1, A 2, A 3 the vertices of a triangle in the Euclidean plane. A point P, whose distances from the sides α1, α2, α3 are in the ratio p 1: p 2: p 3 will be denoted by P[p 1]. p 1, p 2, p 3 are called the normal coordinates of P. Thus the unit point E[l] is the incentro of the triangle, S[cosec α1] is the centroid, M[cos α1] is the circumcentre, and H[sec α1] is the orthocentre. Similarly, using normal line coordinates, we have l 0 [l] is the unit line, l ∞[sin α1] is the line at infinity and lH [cos α1] is the axis of the altitudes.