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If $γ = 16 \sin \frac{π}{9} \sin \frac{2 π}{9} \sin \frac{3 π}{9} \sin \frac{4 π}{9}$ $α = \cos \frac{π}{7} + \cos \frac{3 π}{7} + \cos \frac{5 π}{7}$ and $β = \cos \frac{2 π}{7} + \cos \frac{4 π}{7} + \cos \frac{6 π}{7}$ then the equation the circle whose center at $(2 α, 2 β)$ and $γ$ is radius is

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$x^{2} + y^{2} + 2 x + 2 y - 7 = 0$

$x^{2} + y^{2} - 2 x + 2 y - 7 = 0$

$x^{2} + y^{2} - 2 x - 2 y - 7 = 0$

$x^{2} + y^{2} + 2 x - 2 y - 7 = 0$

answer is B.

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Detailed Solution

$2 α = 1, 2 β = - 1, γ = 3$

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