Let the coordinates of A, B and C be (x1, y1), (x2, y2) and (x3, y3). See Fig.. Suppose L is the line whose equation is L = ax + by + c = 0 meeting the sides in D, E and F. Therefore, we get
Hence
BD/DC.CE/EA.AF/FB
Note: Either the line l meets all three sides externally or two sides internally and one side externally. That is why product of the ratios is equal to −1.