Connect.-.the.-.dots

Nine dots are drawn on a unit grid. We want to connect them with straight lines without taking the pencil off the paper so as to maximize the total resulting length :

• a line is a segment bewteen two dots.
• there should be eight lines in total.

The resulting length can be written as $a\phi+b\delta+c$ where $a,b,c$ are integers, $\phi=\frac{1+\sqrt{5}}{2}$ is the golden ratio and $\delta = 1+\sqrt{2}$ is the silver ratio . Submit $a+b+c$