Overlay Issue with direct selection points

I've somehow managed to remove the purple overlay handles and corner points for rounding a shape when direct slecting something(n).  These are ovbiously very crucial and I'd like to be able to see them again.  They appear when I drag a selected anchor point but disappear again as soon as I let go of left-click.  My assumption is I accidently hit a 4 button combo and changed that setting.

Any assistance with this would be greatly appreciated