How does one find an exterior angle bisector relative to the x-axis? Let's say we're given points $A$, $B$, and $C$, which form $\Delta ABC$. Assuming $A=(0,0)$, what is the value of the exterior angle bisector formed by $\angle A$ relative to the x-axis?

(The image is simply to make what I'm asking clearer.)

if you define two unit vectors in the direction of AB and -AC, you could use the fact that the angles between the bisector- let's call it X- and the two lines are equal, and so is the cosine. Using the dot product: $ \ u \cdot X = v \cdot X  $, where u and v are the unit vectors. Once you get a subspace of vectors that satisfy that condition is easy to get the angle with the horizontal axis.
