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Let the triangle be ABC and the centre of the circle be O.
By sine rule
Therefore, angle AOB = 120 degrees and angle ABO = 30 degrees.
So
AO is the radius. Let it be r. AB is the side of the triangle. Let it be a.
So a =
r.
That means the radius of the circle is
The side a is therefore
.
The area of the triangle is
= 