Circle area

Each small circle has a radius that measures 1/2 of the radius of the large circle. Therefore, each small circle's area is 1/4

the area of the big circle. Therefore, the total area of the four small circles is equal to that of the big circle. The area of overlap between the four small circles, which is shown in blue, must be equal to the area that the four small circles do not cover in the large circle, the green regions. Therefore, the blue and green regions have equal areas.

Why do the blue shaded area must be equal to the area that the four small circles do not cover in the large circle? I only can prove this by doing calculations, cant figure it out with logic..... your help is much appreciated :)

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$