s[1]={s11,s12};
s[2]={s21,s22};
s[3]={s31,s32};
a[i_,j_]=s[i]+(s[j]-s[i])/(1-r[j]/r[i]);
Det[{a[1,2]-a[1,3],a[1,3]-a[2,3]}]

s11=0;s12=0;s21=5;s22=1;s31=0;s32=4;r[1]=2.01;r[2]=1;r[3]=0.52;
Graphics[{Table[Circle[s[i],r[i]],{i,3}],
Point[a[1,2]],Point[a[1,3]],Point[a[2,3]],
Line[{a[1,2],a[1,3],a[2,3]}]}]