[tex]\frac{2}{a}=\frac{b}{3}=\frac{3}{a+c}=k\\ \\ \Rightarrow a=\frac{2}{k}\\ \\ b=3k\\ \\ a+c=\frac{3}{k}\\ \\ \frac{2}{k}+c=\frac{3}{k} \Rightarrow \frac{2}{k}+\frac{kc}{k}=\frac{3}{k} \ |\cdot k\\ \\ 2+kc=3 \Rightarrow kc=3-2 \Rightarrow c=\frac{1}{k}\\ \\ bc=3k\cdot \frac{1}{k}=3[/tex]
