SOLUTION: A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of the circle. What is the ratio of the area of the squ

Algebra ->  Circles -> SOLUTION: A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of the circle. What is the ratio of the area of the squ      Log On


   

Question 546953: A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of the circle. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fraction in terms of pi.
Note: the diagram is a square, with a circle that has a diameter bigger than the square, and there are eight points where the circle intersects, 2 on each side of the square. From what i understand, the radius of the circle extends from the center out past the edge of the square, and the chord is only a fraction of one side of the square.Help? Thank you very much.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
r=AB=AC=BC, AD=r%2F2, ED=DF=CD=sqrt%283%29%2Ar%2F2, EF=sqrt%283%29%2Ar
The area for the square is %28EF%29%5E2=%28sqrt%283%29%2Ar%29%5E2=3r%5E3
The area for the circle is pi%2Ar%5E2.
The ratio would be 3%2Fpi