Make |PA|=|PB|=m

The radius of the circle r= 1

Then sin (a/2) = r/po =1√ (m2+1) (o is the center).

cosa= 1-2sin^(a/2)= 1- 1/(m^2+ 1)=(m^2- 1)/(m^2+ 1)

Vector Pa * Pb = | Pa | | Pb | * COSA

=m^2 *(m^2- 1)/(m^2+ 1)

=(m^4-m^2)/(m^2+ 1)

Let the vector Pa * Pb = n.

Then (m 4-m 2)/(m 2+ 1) = n

m^4-(n+ 1)m^2-n=0

δ=(n+ 1)^2+4n>； =0

Solution: n> =-3+2 √ 2n <; =-3-2√2 (omitted)

So the minimum value is -3+2√2.