Four coplanar points on a skew quadrilateral

Question

$P,Q,R,S$ are four coplanar points on the sides $AB,BC,CD,DA$ of a skew quadrilateral. The product $\frac{AP}{PB}.\frac{BQ}{QC}.\frac{CR}{RD}.\frac{DS}{SA}$ equals?

My attempt:

I was not able to even start the problem, because I have never worked on a skew quadrilateral. Any hints would be helpful.

Answer 1

My answer would be $1$. For coplanarity all points must lie at same height from base of cuboid that creates skew quadrilateral.

Answer 2

This is not an ideal solution but rather a "fake solve".

Consider point D to coincide with point A(we may assume $D \rightarrow A, and \lim_{D \rightarrow A} \frac{DS}{SA} =1$. Then in $∆ABC$, the answer is just $1$ due to Ceva's theorem.

I am looking forward to a proper solution.