(A) $(\frac{\sqrt{3}-1}{2\sqrt{2}},\frac{\sqrt{3}+1}{2\sqrt{2}})$

(B) $(\frac{\sqrt{3}+1}{2\sqrt{2}},\frac{\sqrt{3}-1}{2\sqrt{2}})$

(C) $(\frac{\sqrt{3}+1}{2\sqrt{2}},\frac{1-\sqrt{3}}{2\sqrt{2}})$

(D) $(-\frac{1}{2},\frac{\sqrt{3}}{2})$

If $P$ and $Q$ are the end points of the diameter, it is quite clear that the equation of the circle must be

$$

Therefore, all the vertices must lie on this circle. Now, checking from the options, we find that every point given in the options satisfies the above equation. Now I am stuck.

How else should I tackle the sum?