In a $△$ ABC, a=1 and the perimeter is six times the A.M of the sines of the angles then measure of $∠ A$ is

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Solution

The correct option is C

1+b+c=6 $\frac{s i n A + s i n B + s i n C}{3}$
= $2 (\frac{1}{2 R} + \frac{b}{2 R} + \frac{c}{2 R}) = \frac{1}{R} (1 + b + c)$
$∴ R = 1 (∵ 1 + b + c \neq 0)$
So, $\frac{1}{s i n A} = 2 R = 2 \Rightarrow A = \frac{π}{6}$

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