I have two vectors (and their two dimensional components): $\vec{AB}$ and $\vec{AC}$ that have the same length.
How can I calculate a vector $\vec{AD}$ components that satisfies
$\angle {DBA} = \angle {DCA} = 90$
$\angle {DAB} = \angle {DAC} $
Basically I need the result vector to be angle bisector of the two vectors, and create two right triangles with the vectors where the right angle in each is in the end point of the vectors (not on the result vector).
This is not homework. its for an application I develop and I have no clue how to solve it.
Edit: an image of what I need with my amazing drawing skills: