Geometric mean of two numbers, say, a and b =
√[a * b]....so .....if we have
x / 4 = 9 / x cross-multiply
x^2 = 9 * 4
x^2 = 36
√x^2 = √36
x = 6 .....this is the geometric mean of 9 and 4
In geometry......if we had
AB/BC = BC/AD
BC^2 = AB * AD
√BC^2 = √[AB * AD ]
BC = √[AB * AD].....so ....BC is the geometric mean of AB and AD