Looking for an inscribed quadrangle in a rectangle with minimal perimeter

Question

I thought up an other math problem, and hope you all will find it interesting.

Given is a rectangle ABCD. The points P on the line AB, Q on BC, R on CD and S on AD are inner points of the rectangle sides.

Inner points of a line are all points of this line except the end points.

Now it shall be determined for which positions of the points P, Q, R and S, the rectangle PQRS has the smallest circumference.

Thanks for all good answers

Answer 1

Maximal surface gives a minimal perimeter, I think. So, S, P, Q, R should be placed in the middle of the rectangular sides.

Answer 2

The rhombus connecting middle points of sides of rectangle. Follows from property of light with equal incidence/reflectance angles at $(P,Q,R,S)$, or, of minimum length/time by Fermat's principle.