Calculating the coordinates of a point on a circles circumference from the radius, an origin and the arc between the points

Let the coordinates of $P_1$ be $(x_{P_1},y_{P_1})$. Let the angle between the points $P_1$ and $P_2$ be $\theta$. Then from the arc $d$ you get, $\theta=d/r=\frac{2\pi}{x}$. So, now, we have $$x_{P_2}=x_{P_1}+r\sin{\theta};\ \\ y_{P_2}=y_{P_1}-r(1-\cos{\theta})$$.