If $\frac ab= \frac bc= \frac cd$ then $(a^2+b^2)(c^2+d^2)=(ab+cd)^2$ [sic?] This is a basic algebra question. I found in class 9 math book and it is little tricky for me.

If $$\dfrac ab= \dfrac bc= \dfrac cd$$
  prove that  $$(a^2+b^2)(c^2+d^2)=(ab+cd)^2$$
Note (by @Blue). As observed in comments, the problem is incorrect as stated. It becomes valid if $(ab+cd)^2$ is replaced by $(ac+bd)^2$, but it is not clear if this is the source's intention. 


Using complex numbers and their absolute value one can transform
$$
(a^2+b^2)(c^2+d^2)=|a-ib|^2|c+ id|^2=|(ac+bd)+i(ad-bc)|^2,$$ 
so with $ad=bc$ the right side is pretty fixed.
