How can I prove that the 2 inner circles in a big circle is half the area of the big and that the 2 inner circles equals the circumference of the big circle?

Answer 1

Te circumference of each small square is πd/2, where d is the diameter of the large circle.

Obviously the two circumferences add to the circumference of the large.

A_large = πr²

A_small = π(r/2)²

A_small = πr²/4

2A_small = πr² / 2

QED