Question 22Let $ABCD$ be a cyclic quadrilateral. The side lengths of $ABCD$ are distinct integers less than $15$ such that $BC\cdot CD=AB\cdot DA.$ What is the largest possible value of $BD?$$\sqrt{\dfrac{325}{2}}$$\sqrt{185}$$\sqrt{\dfrac{389}{2}}$$\sqrt{\dfrac{425}{2}}$$\sqrt{\dfrac{533}{2}}$