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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