Let ABC be a triangle with area S and points D,E,F on the sides BC,CA,AB. Perpendiculars at points D,E,F to the BC,CA,AB cut circumcircle of the triangle ABC at points (D1,D2),(E1,E2),(F1,F2). Prove that:
|D_1B\cdot D_1C \minus{} D_2B\cdot D_2C| \plus{} |E_1A\cdot E_1C \minus{} E_2A\cdot E_2C| \plus{} |F_1B\cdot F_1A \minus{} F_2B\cdot F_2A| > 4S inequalitiesgeometrycircumcirclegeometry proposed