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We have a circle with the known radius $r$ and the circumference $2\pi r$, and we know a point $P_1$ somewhere on it's circumference. Now, we want to get the coordinates $[x_{P_2},y_{P_2}]$ of the point $P_2$. We know the arc between $P_1$ and $P_2$ as $d = \frac{2\pi r}{x}$ where $x$ is known and $\geq 1$.

As a matter of fact, by knowing $d$ we know the angle from the center between $P_1$ and $P_2$, but I am unable to find a formula to get me the correct coordinates of $P_2$ for any combination of known $P_1$, $r$ and $d$.