A) \[{{b}^{2}}=ac\]
B) \[2b=a+c\]
C) \[2ac=b(a+c)\]
D) \[a+b=c\]
Correct Answer: B
Solution :
Since, \[\tan \frac{A}{2}=\frac{5}{6}\]and \[\tan \frac{C}{2}=\frac{2}{5}\] \[\therefore \] \[\tan \frac{A}{2}\tan \frac{C}{2}=\frac{5}{6}.\frac{2}{5}\] \[\Rightarrow \]\[\sqrt{\frac{(s-b)(s-c)}{s(s-a)}}\times \sqrt{\frac{(s-a)(s-b)}{s(s-c)}}=\frac{1}{3}\] \[\Rightarrow \] \[\frac{s-b}{s}=\frac{1}{3}\] \[\Rightarrow \] \[3s-3b=s\] \[\Rightarrow \] \[2s=3b\] \[\Rightarrow \] \[a+c=2b\]You need to login to perform this action.
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