In the diagram, $ABCD$ is a square. Find $PR.$

The side length of the square is 10. L, M, N, O are midpoints.

Here's the same problem with a side of 12

https://web2.0calc.com/questions/square_34 (proyaop's answer )

See if you can follow the reasoning with your problem

Hint : I believe that your "PR" will be (10/12) of what was found in this link