Avem cercurile O1,O2,respectiv O3, cu razele R1,R2,R3 si punctele de contact cu tangenta comuna d respectiv,A, B si C.
AB=AC+BC
(R1+R2)2=AB2+(R1-R2)2 ; AB2=4R1R2
(R2+R3)2=BC2+(R2-R3)2 ; BC2=4R2R3
(R1+R3)2=AC+(R1-R3)2 ;AC2=4R1R3
4R1R2=4R2R3+4R1R3+4R3(R1R2)1/2
R3=R1R2/(R1+R2+(R1R2)1/2)
In cazul nostru ar fi
R3=2/(3+21/2)