2019 Cayley Problem 20

In the diagram, each of the circles with centres X, Y and Z is tangent to the two other circles. Also, the circle with centre X touches three sides of rectangle PQRS and the circle with centre Z touches two sides of rectangle PQRS, as shown.

If XY = 30, YZ = 20 and XZ = 40, the area of rectangle PQRS is closest to

\textbf{(A)}\ 3900\quad \textbf{(B)}\ 4100\quad \textbf{(C)}\ 4050\quad \textbf{(D)}\ 4000\quad \textbf{(E)}\ 3950

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.