repeated pbm but simple for others

answer will be (2+3√2+3)/2

i have done a method and i cant complete it

let P and Q be two pts on the circle x2+y2=4 and (x-3)+(y-3)2=9 respectively and the diameter of the smallest circle shud be the maximum distance between P and Q

there P(h,k) and Q(p,q)

(h-p)²+(k-q)²=l²

and i dont know how to proceed after this and i have only two eqns but 4 knowns i cant find any other eqns can anyone find a ways to this method please post

and if u got any other method please post

u both given correct ans
can u explain me

i think it should be 5 units, draw the 2 circles on the coordinate plane nd u'ii find

join (0,0) and (-3,-3) (the centres) extend it to meet the circles,you should get the diameter which is 5+3√2

no but the correct ans was given by pankaj sir and vivek_aero