In[]:=
h=(x-1)^2+(y-1)^2+(z-3)^2-4;g=x-1;i=(x-2)^2+(y-2)^2+(z-1)^2-2;ContourPlot3D[{h==0,g==0,i==0},{x,-5,5},{y,-5,5},{z,-5,5},MeshFunctions{Function[{x,y,z,i},i-g]},MeshStyle{{Thick,Blue}},Mesh{{0}},ContourStyleDirective[Orange,Opacity[0.5],Specularity[White,30]],PlotPoints60,SphericalRegionTrue]
Out[]=
