the value of $M+u(1, 1)$

Question

Consider the domain $\Omega=\{(x,y): (x-1)^2+(y-1)^2<4 \}$ and let $\partial \Omega$ be its boundary. Let $u$ be the solution of the following Dirichlet problem \begin{alignat*}{2} \nabla ^2u & = 0 && \ \ \textrm{ in $\Omega$} \\ u & = x && \ \ \textrm{ on $\partial\Omega$} \end{alignat*} If $M=\displaystyle\max_{(x,y)\in\Omega\cup\partial\Omega} u(x, y)$, then what is the value of $M+u(1, 1)$, where $(1,1)\in\Omega$. How do I find the value of $u(1,1)$? Thanks