Problem

Source: 2010 Saudi Arabia IMO TST III p2

Tags: perpendicular, geometry



Let $ABCD$ be a convex quadrilateral such that $\angle ABC = \angle ADC =135^o$ and $$AC^2 BD^2=2AB\cdot BC \cdot CD\cdot DA.$$Prove that the diagonals of $ABCD$ are perpendicular.