If a triangle inscribed in a circle has area 40, what is the

(1)
This statement tells us that the inscribed triangle is a right angled triangle.
Right angled triangle have three sides;
Two smaller sides and one hypotenuse.

Area = 1/2*(smaller side)*(bigger side)=40 if we assume that it is not an isosceles right triangle.

We know the radius = 1/2*(Diameter) = 1/2*(Hypotenuse) [Hypotenuse is referred as "BASE" in this statement]
Not Sufficient.

(2)
The measure of one of the angles in the triangle is 30.
We can make plenty such triangles with one angle as 30.
Not sufficient.

Combining both;

We know that the triangle is a right angled triangle with 30-90-60 as its angles.

The opposite sides will be in ratio: \(x:2x:\sqrt{3}x\)

\(Area = \frac{1}{2}*x*\sqrt{3}x=40\)
\(x^2=\frac{80}{\sqrt{3}}\)
\(x=\sqrt{\frac{80}{\sqrt{3}}}\)

\(Hypotenuse = Diameter = 2x= 2*\sqrt{\frac{80}{\sqrt{3}}}\)
\(Area = \pi*(\frac{Diameter}{2})^2=\pi*(\sqrt{\frac{80}{\sqrt{3}}})^2=\pi*\frac{80}{\sqrt{3}}\)

Sufficient.

Ans: "C"