I need to write a proof for the following problem. Let theta be an arbitrary angle and suppose the length of the internal angle bisector to that angle and the length of the inradius are given. Perform the construction, discuss the number of possible triangles and give the conditions for each.
I started by constructing the angle given, and bisecting it and making the length of the bisector the length given. From there, I dropped perpendiculars to the sides of the vertex from the bisector, since the center of the incircle will lie somewhere on the angle bisector. Is this correct? Or how can I go about this? I also am not sure about the last portion of the questions regarding the conditions.