Question

What is the area of the large square?

Answer 1

let the distance between length 4 and center of the figure be x
let the distance between length 6 and center of the figure be y
then 4+x=6+y or x=y+2 (1)
form the inner circle (6+y)*y=x*x (2)
from (1) and (2) x=4 and y=2
therefore length of smaller square is 8 and of larger square 16
thus area of larger square is 256

Comments

why  (6+y) *y = x*x ?

Answer 2

Let the radius of large circle = r
For small circle apply intersection of the chord theorem . That is When two chords intersect each other inside a circle, the products of their segments are equal.
hence
r * (r-6) = (r-4) * (r-4) solving r = 8
So area = 2r * 2r = 256

Answer 3

this is a theorem.