isosceles hunt 3

Which figure contains more isosceles triangles? [br][br](Scroll down to explore in an applet or get a more accurate figure.)
In the following applet, drag the point E to change this figure.[br][br]Which triangles must be isosceles no matter how you drag E?[br][br](By the way, do you notice how this figure is drawn in GeoGebra?)

Information: isosceles hunt 3