The sides of a triangle inscribed in a given circle .Subtend angles of $\alpha,\beta$ and $\gamma$ at the centre.The minimum value of the arithemetic mean of $\cos(\alpha+\pi/2),\cos(\beta+\pi/2)$ and $\cos(\gamma+\pi/2)$ is equal to

Question

$(a)\;-\large\frac{\sqrt 3}{2}\qquad$$(b)\;\large\frac{1}{\sqrt 2}$$\qquad(c)\;\large\frac{2}{3}$$\qquad(d)\;\large\frac{3}{2}$