Sections in the sphere

In the initial position of the applet it represents a circle, and when you move the cursor changes the vertical position of a chord. You could here think about the arithmetic mean and the geometric mean of two magnitudes and see that the geometric mean is less than or equal to the arithmetic mean. Both agree only if the two quantities are equal.

But here we see the sections in one sphere. Simply click on the picture and drag to see the representation of a sphere and one section.

If x is the distance from the center of the sphere to the section, the radius of the section is

And the area of the section is