If sides $\displaystyle L_{r}\equiv x\cos \alpha_{r} + y\sin \alpha_{r} = 0, r = 1, 2, 3$ enclose a triangle, then show that $\displaystyle L_{1}\cos (\alpha_{2} - \alpha_{3}) = L_{2}\cos (\alpha_{3} - \alpha_{1}) = L_{3}\cos (\alpha_{1} - \alpha_{3})$ gives the orthocentre of the triangle.