I would say yes this is very doable (but can't help right now). I would do a search on either "arcpy split along line" or split line at point, or some of the other terms similar. Questions that would help others...
- Do you already know the apex (i.e. maybe separate point layer)
- are the distances the same for 1) each apex, 2) each line/direction
You should look at Geometry—Help | ArcGIS for Desktop You can do just about anything in a python script with this, that is breaking any feature down to it's smallest part, basically an x/y coordinate. But someone may have already written something to I would look around on the web.
The "official" code sharing page from esri now is here: ArcGIS Code Sharing