If you want each of your circles to have the same number of points/plots on them, then just use the formula
$$
(x, y) = \left( (50 - kr)\cdot\cos\left(n\cdot\frac{2\pi}{p}\right) + 50, (50 - kr)\cdot\sin\left(n\cdot\frac{2\pi}{p}\right) + 50 \right)
$$
where $p$ is the number of plots that you want, $n$ ranges between $0, 1, \ldots, p-1$ to give you equally spaced points around the circle(s), $r$ is the distance between the different sized circles, and $k$ ranges from $0$ to the integer part of $50/r$ where $k = 0$ corresponds to the largest circle, $k=1$ corresponds to the next largest circle, and so on. Is this what you're after?
Example. Suppose you want eight equally spaced points, so that $p = 8$. Then you have the following cosine and sine values:
$$
\begin{array}{r|c|c|c|c|c|c|c|c}
n & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7\\\hline
\cos(2n\pi/8) & 1 & 1/\sqrt{2} & 0 & -1/\sqrt{2} & -1 & -1/\sqrt{2} & 0 & 1/\sqrt{2}\\
\sin(2n\pi/8) & 0 & 1/\sqrt{2} & 1 & 1/\sqrt{2} & 0 & -1/\sqrt{2} & -1 & -1/\sqrt{2}\\
\end{array}
$$
These can be determined quickly by using Excel (or some variant), especially for other values of $p$. Thus, the coordinates on the largest circle are
$$
\begin{array}{cc}
(100, 50), & \big((50/\sqrt{2}) + 50, (50/\sqrt{2}) + 50\big),\\
(50, 100), & \big((-50/\sqrt{2}) + 50, (50/\sqrt{2}) + 50\big),\\
(0, 50), & \big((-50/\sqrt{2}) + 50, (-50/\sqrt{2}) + 50\big),\\
(50, 0), & \big((50/\sqrt{2}) + 50, (-50/\sqrt{2}) + 50\big),\\
\end{array}
$$
or, in decimal,
$$
\begin{array}{cc}
(100, 50), & (85.3553, 85.3553),\\
(50, 100), & (14.6447, 85.3553),\\
(0, 50), & (14.6447, 14.6447),\\
(50, 0), & (85.3553, 14.6447).\\
\end{array}
$$
If your distance to the next largest circle is $10$, then the coordinates are
$$
\begin{array}{cc}
(90, 50), & \big((40/\sqrt{2}) + 50, (40/\sqrt{2}) + 50\big),\\
(50, 90), & \big((-40/\sqrt{2}) + 50, (40/\sqrt{2}) + 50\big),\\
(10, 50), & \big((-40/\sqrt{2}) + 50, (-40/\sqrt{2}) + 50\big),\\
(50, 10), & \big((40/\sqrt{2}) + 50, (-40/\sqrt{2}) + 50\big),\\
\end{array}
$$
or, in decimal,
$$
\begin{array}{cc}
(90, 50), & (78.2843, 78.2843),\\
(50, 90), & (21.7157, 78.2843),\\
(10, 50), & (21.7157, 21.7157),\\
(50, 10), & (78.2843, 21.7157).\\
\end{array}
$$
All decimal values have been rounded to four significant figures. I hope it is clear now how one might continue, and do the same with different values for $p$.
Excel Spreadsheet. The following image gives a small example of what I would do to generate the points. I have included the equations for cells B$3$, B$4$, B$6$, and B$7$ at the bottom --- these can be dragged across to apply to all cells in the range that you require. Then you can change the values for $p, k, r$ to get the points on different circles according to which circle you want the coordinates for.
I hope it makes slightly sense. Thank you in advance.
