isi-entrance 2017 Q24

isi-entrance · India · UGA Circles Inscribed/Circumscribed Circle Computations
Let $P = \left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ and $Q = \left(-\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}}\right)$ be two vertices of a regular polygon having 12 sides such that $PQ$ is a diameter of the circle circumscribing the polygon. Which of the following points is not a vertex of this polygon?
(A) $\left(\frac{\sqrt{3}-1}{2\sqrt{2}}, \frac{\sqrt{3}+1}{2\sqrt{2}}\right)$
(B) $\left(\frac{\sqrt{3}+1}{2\sqrt{2}}, \frac{\sqrt{3}-1}{2\sqrt{2}}\right)$
(C) $\left(\frac{\sqrt{3}+1}{2\sqrt{2}}, \frac{1-\sqrt{3}}{2\sqrt{2}}\right)$
(D) $\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$.
Let $P = \left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ and $Q = \left(-\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}}\right)$ be two vertices of a regular polygon having 12 sides such that $PQ$ is a diameter of the circle circumscribing the polygon. Which of the following points is not a vertex of this polygon?\\
(A) $\left(\frac{\sqrt{3}-1}{2\sqrt{2}}, \frac{\sqrt{3}+1}{2\sqrt{2}}\right)$\\
(B) $\left(\frac{\sqrt{3}+1}{2\sqrt{2}}, \frac{\sqrt{3}-1}{2\sqrt{2}}\right)$\\
(C) $\left(\frac{\sqrt{3}+1}{2\sqrt{2}}, \frac{1-\sqrt{3}}{2\sqrt{2}}\right)$\\
(D) $\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$.