probability or statistics - Is this TransformedDistribution beyond Mathematica?

Creating the following transformed distribution $A$

A = TransformedDistribution[Sqrt[x^2], x \[Distributed] NormalDistribution[\[Mu], \[Sigma]]]

and then using A to create another TransformedDistribution $B$,

B = TransformedDistribution[1/2 + Sqrt[c^2 d^2 (d^2 - c x^2)]/(2 c d^2), x \[Distributed] A]

seems to get Mathematica stuck on

PDF[B, x]

Or is it me doing something wrong?