First..In this question the triangle is not inscribed in the Circle. "Inscribed" in Planar geometry means the end points of the triangle must touch the circumference of the circle.
In this case:
Imagine a circle with Centre O. There are 2 points on the circle A and B. There you have your triangle, OAB. since OA and OB are the radii of the circle both are equal to 1.
Now we have to find out the maximum possible area of this Triangle.
Area = 1/2 * Base * Height.
If you take OA as the base, we have to find out what is the maximum height possible for this triangle with B on the Circle.
By simple imagination it can be found out that the max hieght is the radius itself, in any other case, the hieght will be less than the radius.
Hence Area = 1/2 * OA * OB.
or 1/2 * 1 * 1
Time to play the game...