Question

If $P(0,0), Q(1,0)$ and $R\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$ are three given points, then the centre of the circle for which the lines $P Q, Q R$ and $R P$ are the tangents is
(A) $\left(\frac{1}{2}, \frac{1}{4}\right)$
(B) $\left(\frac{1}{2}, \frac{\sqrt{3}}{4}\right)$
(C) $\left(\frac{1}{2}, \frac{1}{2 \sqrt{3}}\right)$
(D) $\left(\frac{1}{2}, \frac{-1}{\sqrt{3}}\right)$

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