OE

Equilateral triangle inscribed in a circle, has got centre of the circle where all medians
intersect.
Medians of equilateral triangle, intersect at a point which divides every median in
the ratio 2:1.
Where part towards the vertex is 2 units and the part towards the side is 1 unit.
Area of equilateral triangle =$\dfrac{\sqrt{3}}{4}$ side^2 $=9 \sqrt{3} = \dfrac{\sqrt{3}}{4}$


In the given equilateral triangle Median/ Altitude / Height of equilateral triangle = √3/2 (𝑠𝑖𝑑𝑒) = √3/2 (6)

Median = 3 √3

If we split 3 √3 , in the ratio 2:1.
It is 2 √3 :1 √3.
So, if we look at the figure part towards upper vertex is 2 √3 units.

Hence a = 2 √3 .
Ans. (A)