Question

In $\Delta ABC$ if $tan\frac{A}{2}=\frac{5}{6}$ and $tan\frac{B}{2}=\frac{20}{7}$ then the side are in.

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P.

Answer 1

Answer: (A)

A.P.

$\tan \frac{A}{2}=\sqrt{\frac{(S-b)(S-c)}{S(S-a)}},\tan \frac{B}{2}=\sqrt{\frac{(S-a)(S-c)}{S(S-b)}}$

$\tan \frac{A}{2}.\tan \frac{B}{2}=\frac{5\times 20}{6\times 7}$

$\frac{a+b-c}{a+b+c}=\frac{50}{21}$

$21a+21b-21c=50a+50b+50c$

$71c+29a+29c=0$

$\tan \frac{A}{2}\tan \frac{B}{2}+\tan \frac{B}{2}.\tan \frac{C}{2}+\tan \frac{C}{2}\tan \frac{A}{2}=1$

$\tan \frac{C}{2}=-\frac{20}{31}$

$\pi /2<\frac{C}{2}<\pi$

$\pi <C<2\pi$

Not possible.