My problem is related to proving that the average distance of random distributed points from the diagonals is less than the average distance from the circumference of the circle.
The problem is related to Computer Networking (specifically Wireless sensor Networks) where using a Diagonal over Circle is being proved. The statement in a published research paper states that-
The average distance to the diagonal is smaller than the ring that leads the shorter request and response paths to the diagonal line than the circumference of the ring, which minimizes the energy consumption and decreases the delivery delay. snapshot of the research paper
Full paper (GoogleDrive link): https://drive.google.com/file/d/15IyjkHEqk7QeuItHtAigVh6tc0bVaa8r/view?usp=sharing
The author has stated the result without any mathematical proof and I want to confirm if that is actually true for all cases or just some special case. I am pretty bad at math and can't even comprehend where to start.
Shape of the area is Rectangle and Points are Randomly scattered in the area