4. Two circles are concentric, with radii $R$ and $r$ ($R>r$). The vertices of the convex quadrilateral $ABCD$ are such that vertex $A$ is on the smaller circle, and vertices $B$, $C$, and $D$ are on the larger circle. The maximum area of the convex quadrilateral $ABCD$ is $\qquad$
4. $R(R+r)$.

As shown in Figure 4, in the convex quadrilateral $ABCD$, $DB$ is the diameter of the larger circle, $AC$ passes through the center $O$, and $AC \perp BD$.