①PD=PA As can be seen from the figure, P is the midpoint of arc AB, PA= root number 2, and radius = root number 2.

②AD=AP means AD=AP=AB=4 and the angle APB = 90, so the triangle APB does not exist.

③DA=DP Let the center of the semicircle be E, and connect DE and AP at F, then AF= 1/2AP. Calculate 0.5AD*AE=0.5DE*AF by area, so AF=4/ root number 5, so AP=8/ root number 5.

To sum up, PA=2 root number 2 or 8 root number 5/5.