A quadrilateral changes shape with the edge lengths constant.
Show the scalar product of the diagonals is constant. If the
diagonals are perpendicular in one position are they always
perpendicular? NRICH has always had good solutions from Madras
College in St Andrew's, Scotland but the solutions to this
problem were truly As a quadrilateral Q is deformed (keeping the
edge lengths constnt) the diagonals and the angle X between them
change. Prove that the area of Q is proportional to tanX.