Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle $ABC$,right-angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt{2}T$ respectively. In the steady state,the temperature of point $C$ is $T_C$. Assuming that only heat conduction takes place,$\frac{T_C}{T}$ is equal to

• A
  $\frac{1}{(\sqrt{2} + 1)}$
• B
  $\frac{3}{(\sqrt{2} + 1)}$
• C
  $\frac{1}{2(\sqrt{2} - 1)}$
• D
  $\frac{1}{\sqrt{3}(\sqrt{2} - 1)}$