Question 115
Let $ABCD$ be a convex quadrilateral such that $\angle ABC = \angle ADC = 135^\circ$ and
$$
AC^2 \cdot BD^2 = 2AB \cdot BC \cdot CD \cdot DA.
$$
Prove that the diagonals of quadrilateral $ABCD$ are perpendicular.
$$
AC^2 \cdot BD^2 = 2AB \cdot BC \cdot CD \cdot DA.
$$
Prove that the diagonals of quadrilateral $ABCD$ are perpendicular.