Let $ABCD$ be a cyclic quadrilateral such that $AB \cdot BC=2 \cdot AD \cdot DC$. Prove that its diagonals $AC$ and $BD$ satisfy the inequality $8BD^2 \le 9AC^2$. Moderator says: Use the search before posting contest problems http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=530783