ABC is a triangle
$$\begin{aligned}
& \mathrm { m } ( \widehat { \mathrm { ABC } } ) = 50 ^ { \circ } \\
& \mathrm { m } ( \widehat { \mathrm { CAB } } ) = 100 ^ { \circ }
\end{aligned}$$
According to the given information, the expression $\frac { | a - b | + | b - c | + | c - a | } { 2 }$ is equal to which of the following?\\
A) a-c\\
B) $a - b$\\
C) $b - c$\\
D) $b - a$\\
E) $\mathrm { c } - \mathrm { b }$