CAYLEY 2019 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 P Q R S and the circle with centre Z touches two sides of rectangle P Q R S, as shown.

Image

If X Y=30, Y Z=20 and X Z=40, the area of rectangle P Q R S is closest to

Answer Choices
A. 3900
B. 4100
C. 4050
D. 4000
E. 3950