Tikz curve node midway in-between curved lines while breaking line

Is there are any easy way to insert a node in between a curved line as shown in the figure? Using node[midway] {$alpha$} would just place the text next to the curves.

Also, is it possible to make sure that these lines stay parallel to each other?

EDIT:
The code I am using is:

defcenterarc[#1](#2)(#3:#4:#5)% Syntax: [draw options] (center) (initial angle:final angle:radius)
    { draw[#1] ($(#2)+({#5*cos(#3)},{#5*sin(#3)})$) arc (#3:#4:#5); }
    begin{tikzpicture}[scale=5]
    coordinate (A) at (0, 0);
    coordinate (B) at (0, .7);
    coordinate (C) at (2, 0);
    coordinate (D) at ($0.75*(B)+0.25*(C)$);
    coordinate (E) at ($0.6*(A)+.4*(B)$);
    scope[rotate=-19, shift=(D)]input{figures/clarky}endscope
    draw[thick] (B) -- (C);
    draw[thick] (A) -- (C);
    draw[dashed] (E) -- (C);
    centerarc[thick, <->, ](C)(179.5:161:2) node[loc=.5, fill=white] {$alpha$};
    centerarc[thick, <->, ](C)(179.5:172.5:1.8);
    centerarc[thick, <->, ](C)(171.5:161:1.8);
    begin{scope}[shift={(-.5, 0)}, scale=.17]
        draw[->] (0, 0) -- (1, 0) node[anchor=west] {x};
        draw[->] (0, 0) -- (0, 1) node[anchor=west] {z};
    end{scope}
        
    end{tikzpicture}

This way the arcs are parallel as suggested however, I did not find a way to use the coordinates in a nice way for this. Using node[midway, fill=white] {$alpha$} puts the node at the bottom of the arc.

documentclass[tikz, margin=3.141592]{standalone}
usetikzlibrary{angles,
                calc,
                quotes}
usepackage{amsmath}

begin{document}
defcenterarc[#1](#2)(#3:#4:#5)% Syntax: [draw options] (center) (initial angle:final angle:radius)
    { draw[#1] ($(#2)+({#5*cos(#3)},{#5*sin(#3)})$) arc (#3:#4:#5); }
    begin{tikzpicture}[scale=5,
my angle/.style = {draw, <->,
                   angle radius = #1,
                   angle eccentricity=1,
                   anchor=center,
                   },
every pic quotes/.style = {inner sep=1pt, fill=white}
                    ]

    coordinate (A) at (0, 0);
    coordinate (B) at (0, .7);
    coordinate (C) at (2, 0);
    coordinate (E) at ($0.6*(A)+.4*(B)$);
%
    draw[thick]    (A) -- (C) -- (B);
    draw[dashed]   (E) -- (C);
pic [my angle=88mm, "$alpha$"]     {angle = B--C--A};
pic [my angle=77mm, "$alpha_{text{eff}}$"]   {angle = E--C--A};
pic [my angle=77mm, "$alpha_i$"]   {angle = B--C--E};
    end{tikzpicture}
end{document}