ILL 1988 Problem 21

Let "AB" and $CD$ be two perpendicular chords of a circle with centre $O$ and radius $r$ and let $X,Y,Z,W$ denote the cyclical order of the four parts into which the disc is thus divided. Find the maximum and minimum of the quantity $$\frac{A(X) + A(Z)}{A(Y) + A(W)},$$ where $A(U)$ denotes the area of $U.$