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Offline Centres

$O = (0, 0), A = (1, 0) and B = (1 / 2, \sqrt{3} / 2)$ then the centre of the circle for which the lines $O A, A B and B O$ are the tangents, is

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

$(\frac{1}{2}, \frac{1}{4})$

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

$(\frac{1}{2}, \frac{\sqrt{3}}{4})$

answer is A.

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Detailed Solution

$O A = A B = O B = 1 \Rightarrow △ O A B$ is equilateral.

Circum centre = Centroid $= (\frac{1}{2}, \frac{1}{2 \sqrt{3}}) .$

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