Bisectrix of a triangle in tikz

Question

I'm trying to make a triangle with its bisectrices. I made the first bisectrix with the command:

\begin{tikzpicture}[scale=3] 
  \coordinate (A) at (1,0);
  \coordinate (B) at (0,0);
  \coordinate (C) at (30:1cm);
  \coordinate (D) at (15:1cm);
  \draw (A) -- (B) -- (C);
  \draw (A) -- (B) -- (D);
  \fill (0,0) circle (0.0 cm) node[ left ]{B};
  \fill (1.0,0.0) circle (0.0 cm) node[ right ]{A};
  \fill (0.86,.5) circle (0.0 cm) node[ right ]{C};
  \fill (0.96,.26) circle (0.0 cm) node[ right ]{D};
  \draw [help lines] (0,0) grid (1,1);
\end{tikzpicture}

But, I can't do the other bisectrices. When I try use the same command, the commands take me away from desire result.

Someone can help me?

Thanks!

Answer 1

One approach to drawing the bisector of $\angle BAC$ with tikz is to define two coordinates, say $AtB$ and $AtC$ on $AB$ and $AC$, respectively, at equal distance from $A$. Then one computes the midpoint of the segment connecting $AtB$ to $AtC$; finally, one draws the line from $A$ to that midpoint. The code may look like this:

\coordinate (AtB) at ($ (A) !1cm! (B) $);
\coordinate (AtC) at ($ (A) !1cm! (C) $);
\coordinate (BACb) at ($ (AtB) !0.5! (AtC) $);
\draw (A) -- (BACb);