Three rods of identical area of cross-section 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 the point C is \[{{T}_{C}}\]. Assuming that only heat conduction takes place, \[\frac{{{T}_{C}}}{T}\] is equal to [IIT 1995]

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