\draw[thick,name path=L1,Turquoise4] (A) circle (2cm); 
\draw[thick,name path=L2,Turquoise4] (B) circle (1cm);
\draw[name path=L3,Azure4] 
  let 
  \p1=(\$(O)-(A)\$), %jari-jari
  \n1={veclen(\x1,\y1)} %panjang jari-jari
  in
  (O) circle (\n1);