Let a 1 , a 2 , a 3 denote the sides α 1 , α2, α 3 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 α 1 , α 2 , α 3 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 α 1 ] is the centroid, M [cos α 1 ] is the circumcentre, and H [sec α 1 ] is the orthocentre. Similarly, using normal line coordinates, we have l 0 [l] is the unit line, l ∞ [sin α 1 ] is the line at infinity and l H [cos α 1 ] is the axis of the altitudes.