Question

If \(p,q\) and \(r\) be the length of perpendiculars from the vertices \(A,B\) and \(C\) of a triangle upon any straight line, prove that

\[a^2(p-q)(p-r) + b^2(q-r)(q-p) + c^2(r-p)(r-q) = 4\triangle^2 \]


Note. \(\triangle \) is for the triangle \(\triangle ABC\)'s area.