Without loss of generality, we may assume that O is the origin and points A, B and C are (x1, y1), (x2, y2) and (x3, y3), respectively. See Fig.. Observe that either all the three lines (bar)AO , (bar)BO and (bar)CO divide the sides BC, CA and AB internally or two of them divide two sides externally and one divides the third side internally. Now, the equations of the lines (bar)AO , (bar)BO and (bar)CO are, respectively, xy1 − x1y = 0, xy2 − x2y = 0 and xy3 − x3y = 0. Therefore, by , we get