A) \[a+c\]
B) \[a+b+c\]
C) \[b+c\]
D) \[a+b\]
Correct Answer: D
Solution :
We know that \[\frac{c}{\sin \,C}=2R\] \[(\because \,\,\angle C={{90}^{o}})\] \[\Rightarrow \] \[c=\,2R\] ?..(i) and \[\tan \frac{C}{2}=\frac{r}{s-c}\] \[\Rightarrow \] \[\tan \,\,{{45}^{o}}=\frac{r}{s-c}\] \[\Rightarrow \] \[r=s-c\] \[\Rightarrow \] \[r=\frac{a+b+c}{2}-c\] \[\Rightarrow \] \[2r=a+b-c\] On adding Eqs. (i) and (ii), we get \[2(r+R)=a+b\]
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