I am trying to find a solution and explanation for the following problem: I need to find the average distance from a point to the points on a circle with a radius $R$
- The distance from the point to the center of the circle is denoted by r
- There's no requirement on $r$ and $R$, i.e., we can have $≥$ (the origin is inside the circle) or $≤$ (the origin is outside the circle).
In addition, I am looking for the average squared distance.
I found this answer to the first part of my question:
Average distance from point to circle
However, I could use some intuition. As someone who studied economics, I know some calculus, but am out of touch with geometry. I would really appreciate if someone could shed some light on the equation (assuming it's correct).