drawing a triangle with specifc arcs

Question

I am about to write down some calculations in LaTeX. To make them more easily understandable, I want to add a geometric figure. Unfortunately, I am really new to Tikz. While I am able to draw lines, rectangles, triangles, name points, etc. I haven't yet drawn something with a precise angle.

I want to draw a triangle with the vertexes A, B and C and a angle bisector (dividing the angle at B).

I know that the angle at the vertex A = 44°, B = C = 68° and that the distances AB = AC.

\begin{tikzpicture}
\begin{scope}
\tkzDefPoint(0,0){B};
\tkzDefPoint(1,-3){C};
\tkzDefPoint(-1,-3){A};

\clip (-2,0.5) rectangle (2,-4);

\draw[step=.5cm,gray,very thin] (-4,-4) grid (4,4);
\draw (-4,0) -- (4,0);
\draw (0,-4) -- (0,4);

\draw[thick] (A) -- (B) -- (C) -- cycle;
\tkzLabelPoints[above](B);
\tkzLabelPoints[below](C);
\tkzLabelPoints[below](A);
\draw (B) circle [radius=3.2cm];
\draw (B) circle [radius = 3.2pt];

\end{scope}
\end{tikzpicture}

But how do I specify that I want the base angle at the Vertex B to be 68° exactly?

Update: In the manual I have found the following method to draw angles: (45:1cm). Unfortunately, this command uses as a start point whatever coordinate have used last. But how do you specify, that I want it to start from B?

Answer 1

Two methods provided (code is self explanatory - I think):

\documentclass[tikz]{standalone}
\usetikzlibrary{angles,quotes}
\usetikzlibrary{shapes.geometric}
\begin{document}
\begin{tikzpicture}
% Draw it manually using polar coordinates (no libraries needed, I used quotes and angles just to draw the angles):
\draw (0,0) coordinate (B) -- ++(68:3cm) coordinate (A) -- ++(68+44:-3cm) coordinate (C) -- cycle
pic["$B$", draw] {angle=C--B--A}
pic["$A$", draw] {angle=B--A--C}
pic["$C$", draw] {angle=A--C--B};

%Using the shapes.geometric library with the "isosceles triangle" shape:
\node[isosceles triangle,
      isosceles triangle apex angle=44,
      minimum width={6cm*cos(68)},
      draw, anchor=left corner, rotate=90] at (3.2,0) {};
\end{tikzpicture}
\end{document}

Answer 2

\documentclass[border=2mm,tikz]{standalone}
\usetikzlibrary{calc}
\begin{document}

\begin{tikzpicture}
\draw[step=.5cm,gray,very thin] (-3,1) grid (2,-3);
\draw[thick](0cm,0cm)coordinate[label={B}](B)
      --(224:3cm)coordinate[label =left:A](A) 
      --++(3cm,0)coordinate[label=right:C](C)
      --(B)--cycle (A)--($(B)!.5!(C)$);
\draw (-3,0) -- (2,0);
\draw (A) circle [radius = 2pt];
\clip (-.5,.5) rectangle (2,-2.5);
\draw (A) circle [radius=3cm];
\end{tikzpicture}

\end{document}