Three circles of radius 1 unit fit inside a square such that the two outer circles touch the middle circle and the sides of the square. Given the centres of the circle lie on the diagonal of the square, find the exact area of the square.

Question

I got the answer 18 + 8root2
but the book says 12 + 8root2
I'm about 100% sure i got it right and the book might have an error but could someone please check for me because this is really bugging me out, thanks.

Answer 1

the distance between the centers of the two outer circles is 4

they are in the diagonal corners, and their centers are √2 from the corners

so the diagonal of the square is
... 4 + 2√2

dividing by √2 to find side length
... 2 + 2√2

squaring
... 4 + 4√2 + 4√2 + 8 = 12 + 8√2

Answer 2

Ahh thank you so much

Answer 3

isn't 12+8√2 one of the side lengths?

and isn't the question asking you to find the exact AREA of the square?

so would you square (length squared is area formula for square) 12+8√2 to get 272+192√2

Answer 4

Could someone explain it entirely to me?