Geometric Mean Theorem with Area Model
Δ ACB is similar to Δ ADC and Δ CDB since they are formed in a semicircle.
Therefore, algebraic similarity gives a/h =h/b and h² = ab.
Geometrically, the square with side = h is the same size as the
rectangle with sides a and b; i.e., the green square and blue rectangle
have equal areas. This diagram also suggests how to construct a square
equal in area to a given rectangle.
Wikipedia has a nice article with the topic: Geometric mean theorem