Angle bisectors in a parallelogram

The applet illustrates thatifin the parallelogram ABCD (AB > AD), the angles' bisectors AE, BF, CG and DH are drawn, which intersect at points K, I, N and G, then the quadrilateral KING is a rectangle, the diagonals of the rectangle KING are parallel to the sides of the parallelogram, and thelength of the diagonal of the rectangle is the difference between the lengths of the sides of the parallelogram.