Exercise 33 Page 607

Let's write the ratio of their circumferences and the ratio of their corresponding radii.

As we can see, both ratios are equal. We can rewrite the theorem mentioned at the beginning for circles as shown below.

Now, let's recall what the Areas of Similar Polygons states.

By using the same diagram we did before, let's make a table where we find the ratio of the areas and the ratio of the corresponding radii.

From the latter table we conclude that the ratio of the areas of two circles is equal to the square of the ratio of their corresponding radii. This is the way we can rewrite the second theorem to apply to circles.