Question

Four equal circles are described about the four corners of a square so that each touches two of the others. The shaded area enclosed between the circles `24/7 cm^2`, find the radius of the circle.

Answer 1

Let the radius of the circle be R
area of 4 sets`= (pi*R^2)/4*4 = pi*R^2 `
area of square`= (2R)^2 = 4R^2`
area of shaded region `= 24/7 `
`4R^2 - pi R^2 = 24/7`
`R^2(4- 22/7) = 24/7`
`R^2(28-22)/7= 2/7`
`R^2*6=24`
`R = sqrt(4) = 2`cm