Is there any way to solve these without knowingn these?
just using the standard properties of triangles & circles?
Yes, I used another approach
Assume the triangle is ABC and O is the center of the circle.
AO, BO and CO divide the triangle ABC into 3 equal isosceles triangles,
when each has an area of 9sqrt(3) / 3 = 3sqrt(3) .
Extending the AO up to BC , we get a height AD , so OD is the height of triangle BOC.
Now assume OD = x , hence DC = x*sqrt(3) and OC=2 *x = R ( ODC is a right triangle 30-60-90 )
the area of ODC = 3sqrt(3) / 2
x*x*sqrt(3) / 2 = 3sqrt(3)/2
x = sqrt(3)
OC = R = 2*sqrt(3) , hence the area of the circle is 12pi