But I have a problem in understanding this paragraph:
Could anyone clarify this for me please?
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There are three types of circles in the question.
In Figure $1$, we see $1$ big circle and $4$ medium circles.
In Figure $2$, we see $1$ big circle, $4$ medium circles and $16$ small circles.
Note that the ratio of the intermediate circles to the big circle is equal to the ratio of small circle to the medium circle since they are scaling of each other.
The ratio of area of shaded circles of Figure $2$ to the ratio of area of circles of Figure $1$ is equal to the ratio of area of $4$ small circle to the area of a medium circle, which is also equal to the ratio of the area of $4$ medium circle to the big circle.