a={0,0};b={2,0};Manipulate[c1=Midpoint[{a,b}];c2=Midpoint[{b,c}];c3=Midpoint[{c,a}];r1=EuclideanDistance[a,b]/2;r2=EuclideanDistance[b,c]/2;r3=EuclideanDistance[c,a]/2;Graphics[{{Transparent,EdgeForm[{Thick,Red}],Triangle[{a,b,c}]},{Dashed,Circle[c1,r1],Circle[c2,r2],Circle[c3,r3]},{Red,Circle[{x,y},r]/.Apollonius[c1,c2,c3,r1,r2,r3]}}],{{c,{3,4}/2},Locator,AppearanceNone},SaveDefinitionsTrue]