C=π- A-B
C=π-π/4-π/6
C= 7π/12
sinC= sin(7π/12)= sin(3π/12+4π/12)=sin(π/4+π/3)= = sin π/4*cos π/3+sin π/3*cos π/4= √2/2 * 1/2 +√3/2 * √2/2= √2/4+ √6/4=
√2+√6/4 ⇒sin C=√2+√6/4
Aplicam teorema sinusurilor:
AB/sin C=2R
R=AB/2* sinC
R=6/2*(√6+√2)/4
R=6/√6+√2/2
R=12/√6+√2
Dupa ce rationalizezi vei obtine:
R=3(√6-√2) cm
