Problem about parallelogram



Problem

In the right figure,ABCD is a parallelogram.The lines AF,BH,CH and DF are the bisectors of the angles A,B,C and D.EFGH is the quadrilateral formed by the four lines.
(1)What quadrilateral is EFGH? Why that?
(2)What figure is ABCD when EFGH is a square?
(3)What figure is ABCD when E,F,G and H meet at the same point.

Drag red point.