The search step with the binary search tree

There is a discussion in the video about whether we can maintain a data structure where we can insert and delete line segments in O(log n) time and also search for the segments intersecting the new line in O(log n) time. All this can be done with a balanced binary search tree. In the video, I had raised some doubts over it because the search is not exactly for a segment of a given slope, but it is for a segment that intersects with the new line. Nonetheless, the usual search routine in a binary search tree will work fine. Look at the Moodle post for more details. I have deleted some parts of the video, which did not make much sense.