Settlers of Catan - What counts as longest road?

Question

My friends and I are new to Settlers of Catan. We had a dispute over what counts as the longest road. Suppose we have a road that is 8 segments long. Between the 4th and 5th segment we have a road coming off it that is 2 segments long, does this count as that person's road being 10 segments long?

Pictured: For the Longest Road, does this count as 8 segments long, or 10?

S           S — — S
 \         /
  \       /
   S — — S
          \
           \
            S

Assuming all roads and settlements are from the same player, where:

S : Settlement  
\ : Road  
/ : Road  
— : Road

The Argument: One friend was arguing that because the road is not broken by another player, it is 10 segments long while another was arguing that the longest road should be able to be taken in 1 trip, so it is 8 segments long. We know that the rule is given as

"The Longest Road is a continuous road connecting two intersections, which consists of at least 5 individual road pieces and is not interrupted by game pieces belonging to other players. It has more individual road pieces than any other connecting road of this type."

But we were unable to determine which it should be.

Answer 1

It's 8 segments. The game rules say:

The first player to build a continuous road (not counting forks) of at least 5 road segments, receives the Special Card “Longest Road”. [...]

so you don't get to count the two-segment fork.

Answer 2

The way I look at it is as if you where drawing a path between two points on the board with your finger. In order to determine the longest path it would be how far you can move your finger between points without lifting it (break in path) or moving over the same path again.

 S ___ ___ S ___ ___ S ___ ___ S ___ ___ S
(A)                  |                  (B)
                     |
                     S
                    (C)

In the example you gave I could move over 6 roads going from point A->C(C->A) or B->C(C->B) and over 8 going from A->B(B-A) and if I attempted to include all 3 points I would have to include 2 sections of road in my path twice which breaks the path.