[Tex/LaTex] How to draw a geometry triangle in LaTeX

Question

Name explicitly used properties from the sketch (for example, parallel lines, equilateral triangles, right angles), and give common calculation rules used.

Helpful calculation rules and methods can be depending on the example:

• Area and Circumferential Formula for Rectangle, Triangle (Heron), Circle, Trapezoid • Angled Sets for Circle and Triangle, Pythagoras
• Use of symmetries, similarity, proportionality
• Setting up equations

Answer 1

with pure tikz, using polar coordinates and intersections:

\documentclass[11pt, tikz, margin=3.141592]{standalone}
\usetikzlibrary{angles, intersections, quotes}

\begin{document}
    \begin{tikzpicture}[
myangle/.style args = {#1/#2}{angle radius=#1, angle eccentricity=#2, draw, font=\footnotesize},
myangle/.default=8mm/0.8
                        ]
\coordinate[label=$B$]      (b);
\coordinate[label=below:$C$](c) at (255:6);
\coordinate[label=below:$D$](d) at (285:6);
    \draw[name path=cbd]    (c) -- (b) -- (d) -- cycle;
    \draw[name path=A]      (b) ++ (250:6) arc (250:330:6);
    \path[name path=B]      (b) -- ++ (315:8.5);
    \draw[name path=ce,
          name intersections={of=A and B, by=e}] (c) -- (e) coordinate[label=right:E];
    \path[name path=C]      (d) -- ++ (0:4.5);
    \draw[name intersections={of=B and C, by=a}] (d) -- (a) coordinate[label=below:A];
    \draw   (b) -- (a);
% angles
\pic [myangle,"$\alpha$"] {angle = c--b--d};
\pic [myangle,"$\alpha$"] {angle = e--a--d};
    \path[name intersections={of=ce and cbd}] coordinate[label=75:F] (f) at (intersection-2);
\pic [myangle=4mm/0.5,"$\cdot$"] {angle = b--f--c};
% small circle
\draw[fill=white] (b) circle[radius=0.5mm];
    \end{tikzpicture}
\end{document}