I was trying to find the average distance between two points on a circle and got the following result. 
Why is my method wrong?
The wrong way of finding the average distance between two points on a circle
algebra-precalculusanalytic geometrycalculuscirclesgeometry
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Best Answer
Your method is wrong because the distribution of possible $x$ and $y$-values isn't uniform ($x$-values close to $\pm r$ are more common than values close to $0$, and $y$-values close to $0$ and $2r$ are more common than values close to $r$). I would personally suggest you use trigonometry and the angle $\angle P_1OP_2$ instead, as that angle is indeed uniformly distributed.