Three rods of identical cross-sectional area and made from the same metal, form the sides of an isosceles triangle $ABC$ right angled at $B$ as shown in figure. The point $A$ and $B$ are maintained at temperature $T$ and $\sqrt{2}T$ respectively, in the steady state. Now, assuming that only heat conduction takes place. The temperature of point $C$ will be

• A

  $\frac{T}{\sqrt{2}+1}$
• B

  $\frac{T}{\sqrt{2}-1}$
• Correct answer
  C

  $\frac{3T}{\sqrt{2}+1}$
• D

  $\frac{\sqrt{3}T}{(\sqrt{2}+1)}$

Hence, the correct answer is option: 'C'.