Step 1: Create Branches

Scripting
f = Segment((0, 0), (0, 2))[br][br]A = Point(f, 0)[br]B = Point(f, 1)[br][br]C = Dilate(Rotate(A, π + π / 4, B), 0.75, B)[br]D = Dilate(Rotate(A, π - π / 4, B), 0.75, B)[br][br]ListOutPut = {Segment(B, C), Segment(B, D)}
Demo

Information: Step 1: Create Branches