If there are two A.M. A1, A2 two G.M. G1,G2 and two H.M. H1,H2 between

This question was asked in Example 6

If there are two A.M. A1, A2 two G.M. G1,G2 and two H.M. H1,H2 between two numbers a and b then prove that
A1H2 = A2H1 = G1G2 = ab