The centroid and a vertex of an equilateral triangle are \( (1,1) \...

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The centroid and a vertex of an equilateral triangle are \( (1,1) \) and \( (1,2) \) respectively. Another vertex of the triangle can be
\( \mathrm{P} \)
(a) \( \left(\frac{2-\sqrt{3}}{2}, \frac{1}{2}\right) \)
(b) \( \left(\frac{2+3 \sqrt{3}}{2}, \frac{1}{2}\right) \)
(c) \( \left(\frac{2+\sqrt{3}}{2}, \frac{1}{2}\right) \)
(d) none of these
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