IMO 1988 LL GRE26

Origin: GRE

Problem

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