I think the answer is 1/2

Any triangle formed inside the circle will have the greatest area when one its angle is right angle or 90.

Since the other two vertices are touching the circle, both the sides would be the radius, therefore it is an isosceles triangle.

Isosceles triangle : 45, 45 & 90 or 1:1:sqrt2


area = (1/2)*1*1 = 1/2

Hence B.

Whats the OA?

For a triangle, with its two sides as radius of a circle, to have maximum area, the two sides(radii) should be at 90 degrees to each other.

hence 1/2 (1/2*1*1)