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from triangle, OC = sqrt (OD^2 - CD^2) = sqrt [12^2 - (6√3)^2] = sqrt[144 -108] = 6

So, circumference of the circle = 2π*r = 12π

I think B. :)
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If a circle is inscribed in equilateral triangle then "length of OA/OB/OD is equivalent to the diameter of circle".
Since OD is given i.e. 12 so radius is 6 and circumference is 12pi.

Option B
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Don't think OD is even required to solve this.

In an equilateral triangle, circumcenter/incenter are the same, which in this case is O.

From AB, AC can be deduced as √3/2*AB = 12*3/2 = 18.

Now circumcenter divides the median or in this case altitude in 2:1 ratio. Hence, OA = 18*1/3 = 6, and circumference of the circle = 2*6*π = 12π

Option B

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Median drawn from a vertex to the opposite vertex in a triangle is in the ratio 2:1.
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