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a square of side length s which is the black square in the circle is inscribed in a circle of radius R right the first part write the area of the square as a function of the radius R of the circle so usually when Im drawing a radius I start here and I draw it out to the area and thats okay but that doesnt really help me figure anything out about the square so really if Im doing these inscribed circle and square problems I want to look at the radius as that now I can probably figure out the length of each side in relationship to the radius so now what I do know is I know that the area of the square is equal to s squared s times s and if I draw a line like that I know I have R and I know that this distance right here is one-half s and I know that this distance here is one half past because it goes from the center of the square which is also the center of the circle to the edge so I know that but a fanger Ian theorem 1/2 s squared plus 1/2 s squared will equal R squared its a squared