Question 1
Let $S$ be a fixed circle of radius $R$, with center $O$. A fixed point $P$ lies inside it, with $OP=d\lt R$. A variable quadrilateral $ABCD$ has its vertices on $S$, and its diagonals $AC,BD$ intersect at $P$ and are perpendicular. Determine the largest and smallest possible perimeter of $ABCD$ in terms of $R,d$.