drawing a triangle with specifc arcs

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}

\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}