Let A ={(x, y) ∈ R × R ∣ 2 x^2+2 y^2-2 x-2 y=1}, B ={(x, y) ∈ R × R ∣ 4 x^2+4 y^2-16 y+7=0} and C ={(x, y) ∈ R × R ∣ x^2+y^2-4 x-2 y+5 ≤ r^2}. Then…

Let $$\begin{aligned} & \mathrm{A}=\left\{(x, y) \in \mathbf{R} \times \mathbf{R} \mid 2 x^2+2 y^2-2 x-2 y=1\right\}, \\ & \mathrm{B}=\left\{(x, y) \in \mathbf{R} \times \mathbf{R} \mid 4 x^2+4 y^2-16 y+7=0\right\} \text { and } \\ & \mathrm{C}=\left\{(x, y) \in \mathbf{R} \times \mathbf{R} \mid x^2+y^2-4 x-2 y+5 \leq \mathrm{r}^2\right\} . \end{aligned} $$ Then the minimum value of $\displaystyle |\mathrm{r}|$ such that $\displaystyle \mathrm{A} \cup \mathrm{B} \subseteq \mathrm{C}$ is equal to :