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Offline Centres

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

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

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

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

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

answer is A.

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Detailed Solution

I is the incentre of $Δ O A B$

$Δ O A B$ is equilateral

centroid is same as incentre

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