Deleting links from polyline.

Discussion created by klim_c on Jun 15, 2011
Latest reply on Jun 16, 2011 by dlee-esristaff
I would appreciate it very much if you give me a clue of how to delete lines from polyline. Please see attached picture. The ABCD polyline is a result of creating FLAT LEFT sided buffer from original line AB, and converting the buffer polygon into ABCD polyline.
I was able to to delete BC, CD and DA lines from ABCD polyline by dissolving ABCD with "Split Line At Vertices" tool, selecting and deleting unwanted lines.
This is an automated process, and it takes forewer when processing freeway lines because of large number of small links (dissolving result) to process.
Instead of processing those numerous tiny links, I would like to process only 4 corresponding lines at points A, B, C and D.
I can do it by using "Split Line at Point" tool, which takes polyline and set of points as an input. 
My question is how to get those A, B, C and D points from ABCD polyline please?
Thank you in advance.