A) a, c, b are in AP
B) a, b, c are in GP
C) b, a, c are in AP
D) a, b, c are in AP
E) a, c, b are in GP
Correct Answer: D
Solution :
\[\because \] \[\tan \frac{A}{2}=\frac{5}{6}\]and \[\tan \frac{C}{2}=\frac{2}{5}\] \[\therefore \] \[\tan \frac{A}{2}\tan \frac{C}{2}=\frac{1}{3}\] \[\Rightarrow \] \[\sqrt{\frac{(s-b)(s-c)}{s(s-a)}.\frac{(s-b)(s-a)}{s(s-c)}}=\frac{1}{3}\] \[\Rightarrow \] \[\frac{s-b}{s}=\frac{1}{3}\] \[\Rightarrow \] \[3s-3b=s\] \[\Rightarrow \] \[2s=3b\]\[\Rightarrow \] \[2b=a+c\] \[\Rightarrow \] a, b, c are in AP.
You need to login to perform this action.
You will be redirected in
3 sec
