Question

In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______

पर्याय

• b² = ac

• a + b = c

• 2b = a + c

• 2ac = b(a + c)

Answer 1

In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then 2b = a + c.

Explanation:

Given, tan`A/2 = 5/6` and tan`C/2 = 2/5`

∴ `tan  A/2. tan  C/2 = 5/6. 2/5 = 1/3`

⇒ `3tan  A/2. tan  C/2 = 1`

⇒ `3sqrt(((s - b)(s - c))/(s(s - a))). sqrt(((s - a)(s - b))/(s(s - c))) = 1`

⇒ `(3(s - b))/s = 1`

⇒ 3s - 3b = s

⇒ 2s = 3b

⇒ a + b + c = 3b

⇒ 2b = a + c