Optimal 4-Point Configuration

Let $\{x_1,x_2,x_3,x_4\}$ be 4 distinct points on the Euclidian plane such that the distance between any two points is at least 1. We want to minimize the average distance beween 2 points: $\min_{\begin{array}{c}\scriptstyle \{x_1,x_2,x_3,x_4\} \in {\mathbb{R}}^2 \\[-4pt] \end{array} } \frac{1}{6} \sum_{\begin{array}{c}\scriptstyle x_i,x_j\\[-4pt] \scriptstyle \space i < j \end{array} } \text{dist}(x_i,x_j).$ If the minimum average distance is expressed as $\large \frac{a+\sqrt{b}}{c},$ where $a$ and $c$ are coprime and $b$ is square-free, submit $a+b+c$ .