Let $M = (\mathbb{R}^2, d)$ be a D793: Standard euclidean real metric space.
The circle in $M$ centered at $x \in \mathbb{R}^2$ with radius $r \in (0, \infty)$ is the D11: Set \begin{equation} S^2_d(x, r) : = \left\{ y \in \mathbb{R}^2 \mid d(x, y) = r \right\} \end{equation}

Let $M = (\mathbb{R}^2, d)$ be a D793: Standard euclidean real metric space.
The circle in $M$ centered at $(x_0, y_0) \in \mathbb{R}^2$ with radius $r \in (0, \infty)$ is the D11: Set \begin{equation} S^2_d(x, r) : = \left\{ (x, y) \in \mathbb{R}^2 : \sqrt{(x - x_0)^2 + (y - y_0)^2} = r \right\} \end{equation}