Move

*A*along the circumference of the semi-circle. What can you say about the relationship between*AD*and the radius of the circle?
The applet above shows the geometric proof of the arithmetic mean geometric mean inequality. The diameter of the circle is

*a*+*b*and the radius is (*a*+*b*)/2. The length*AD*is less than or equal to the radius of the circle. The complete explanation of the inequality can be found here.