So, we know one point is at the center. We may think of the other two points sliding freely around the circle, but for simplicity's sake, let's "nail" one of them down to the 0 degree point on a standard unit circle. The last point's position can be thought of relative to this point, so it does not matter where we placed it.
Let us also constrain our thinking to 0 through 180 degrees (0 though pi radians), since moving beyond that will merely create a mirror image of a triangle previously obtained.
So, what's the formula for any triangle? 1/2*b*h. We know the base: the line from the center to the 0 degree point; in other words, the radius of the circle, 1. So, our job becomes maximizing h. Well, what is h? h is the y-coordinate of the final point that we're swinging around, the height of the triangle. It becomes fairly obvious that this height is achieved at 90 degrees, where the y-coordinate is 1.
So, 1/2*1*1 = 1/2. B.
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