tan(A+B) = tan(180-C)=-tanC=$\frac{1}{3}$
tan²C+1=$\frac{1}{cos²C}$
=>(-$\frac{1}{3}$)²+1=$\frac{1}{cos²C}$
=>cos²C=$\frac{9}{10}$ =>sin²C=1-cos²C=$\frac{1}{10}$ =>sinC=$\frac{1}{√10}$
$\frac{AB}{sinC}$=2R <=>$\frac{12}{$\frac{1}{√10}$ }$ =2R<=> 12√10=2R =>R=6√10