A piece of paper has the precise shape of an equilateral triangle ABC which is creased along a line XY, with X on AB and Y on AC. so that A falls on some point D on BC.
(i) Are the triangles XBD and DCY always similar?
If so, prove it. If not, give a counterexample.
(ii) If AB = 15 and BD = 3, what is the length of the crease XY?