Steiner mapping of three points on Euclidean plane

For Euclidean plane $\mathbb{C}$ we consider the Steiner mapping associating any three points $a, b, c$ with their median $s$ and the corresponding operator $P_D$ of metric projection of the space $l_1^3(\mathbb{C})$ onto its diagonal subspace $D=\{(x, x, x) \colon x \in \mathbb{C}\}$, $P_D(a, b, c)=(s, s, s) \colon s$. The exact value of the linearity coefficient of $P_D$ is calculated.