Question

In $△ABC,2\tan \frac{A}{2}\tan \frac{C}{2}=1$ then $a,b,c$ are in

• A. AP
• B. GP
• C. HP
• D. none of these

Answer 1

Answer: (D)

none of these

given in $△ABC,2\tan \frac{A}{2}\tan \frac{C}{2}=1$

$⟹2\times \sqrt{\frac{(s-b)(s-c)}{s(s-a)}}\times \sqrt{\frac{(s-a)(s-b)}{s(s-c)}}=1$

$⟹2\times \frac{s-b}{s}=1$

$⟹2s-2b=s$

$⟹s=2b$

$⟹2s=4b$

$⟹a+b+c=4b$

$⟹a+c=3b$

No relation between $a,b,c$