[Tex/LaTex] Draw isosceles triangle with angles and stuff in TikZ

Question

\begin{center}
\begin{tikzpicture}

\draw [line width=1pt, fill=yellow!2] (-1,-3.5) -- (9,-3.5) -- (9,3.5) --     (-1,3.5) -- cycle;

\coordinate (A) at (0,0);
\coordinate (B) at (8,-2);
\coordinate (C) at (8,2);




\draw [line width=1.5pt, fill=white] (A) -- (B) -- (C) -- cycle;


\end{tikzpicture}
\end{center}

Ok well, I neeeeeed your help. How do I draw this piece in TikZ?

I tried things with arc but I have no idea how to draw the lines in the triangle. Thanks in advance for your help.

Answer 1

pure tikz solution:

\documentclass[tikz, border=3mm]{standalone}
\usetikzlibrary{angles, arrows.meta,
                intersections,
                quotes}

\begin{document}
    \begin{tikzpicture}[
my angle/.style = {draw,very thin, Straight Barb-Straight Barb,
                   angle radius=5mm,
                   angle eccentricity=0.75,
                   font=\footnotesize
                   } % angle label position!
                        ]
\coordinate[label= left:A] (A);
\coordinate[label=right:B] (B) at ( 7.5:8);
\coordinate[label=right:C] (C) at (-7.5:8);
%
\draw[gray] (10:8) arc (10:-10:8);
%
\draw[name path=b1, line width=1pt] (A) -- (B) -- (C) -- cycle;
\pic [my angle, "$\gamma$"]   {angle = A--B--C};
%
\path[name path=a1] (C) -- + (37.5+90:2.5);
\draw[name intersections={of=a1 and b1, by={B'}}]
            (C) -- (B') node[above] {B'};
\pic [my angle, "$\alpha$"]   {angle = C--B'--B};
%
\path[name path=a2] (B') -- + (7.5+240:2);
\draw[name intersections={of=a2 and b1, by={notused,C'}}]
            (B') -- (C') node[below] {C'};;
\pic [my angle, "$\alpha$"] {angle = C'--B'--C};
%
\path[name path=a3] (C') -- + (7.5+90:2);
\draw[name intersections={of=a3 and b1, by={B''}}]
            (C') -- (B'') node[above] {B''};
\pic [my angle, "$\alpha$"] {angle = B''--B'--C'};
\pic [my angle, "$\cdot$"]  {angle = A--B''--C'};
\pic [my angle, "$\beta$"]  {angle = C--C'--B'};
\pic [my angle, "$\beta$"]  {angle = B''--C'--A};
    \end{tikzpicture}
\end{document}