Two side-by-side squares are inscribed in a semicircle as shown above.

Side or larger square = a, side of smaller square = b, OX = c

r^2 = a^2 + (a-c)^2
r^2 = b^2 + (b+c)^2

=> a^2 + (a-c)^2 = b^2 + (b+c)^2
=> 2*a^2 - 2ac = 2*b^2 + 2bc
=> a^2 - b^2 = c(a+b)
=> a-b = c

Substitute in any equation, r^2 = a^2 + (a-(a-b))^2 = a^2 + b^2 => a^2 + b^2 = 100

or,

we can obtain the result in a generalized manner. since no specific ratio has been given with respect to the sides of the squares, let's consider them to be of equal size.

So the common side will be perpendicular at origin.
Let side of each square be x.

r^2 = x^2 + x^2 = 2*x^2

2*x^2 is nothing but the combined area of the squares, which is equal to 100.

Ans: C