Given a triangle ABC in which ∣AB∣>∣AC∣. Let P be the midpoint of the side BC, and S the point in which the angle bisector of ∠BAC intersects that side. The parallel with the line AS through the point P intersects lines AB and AC at points X and Y respectively . Let Z be the point be such that Y is the midpoint of the length XZ and let the lines BY and CZ intersect at point D. Prove that the angle bisector of ∠BDC is parallel to the lines AS. geometryangle bisectorparallel