√ab & lt； Geometric meaning of 2/2 a2/ 1B2

The right-angled side AC≠BC of Rt⊿ABC in figure 1,

CH is the height on the hypotenuse, AH=a, BH=b, then CH=√ab (projective theorem),

CM is the center line on the hypotenuse, CM=(a+b)/2,

When a and b are both positive numbers, the geometric meaning of √ ab < (a+b)/2 is

In Rt⊿CH