A 12 m long wire is cut into two pieces. One of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

Answer 1

Length of the square is X and R = (1/2)X

4X + 2 * Pi * R = 12

4X + 2 * PI * (1/2)X = 12

4x + pi * X = 12

(4+pi)*X = 12

X = 12 / (4 + pi) , which is approximately 1.68029746053467212.....+

The radius is HALF of that: 6/(4+pi) = 0.84014873026733606386571793822943....+