transformers(cycli quadrilleterals in disguise)

[Tahmid Hasan]

$ABCD$ is a trapezoid with $AD \parallel BC$ and $BC=BD$,$$CD<BC$$ and$$\angle BAC+\angle BDC=\pi$$.express $CD$ as a function of $BC$.(hint:read the topic name )

[*Mahi*]

Are you sure your question is right? $\angle BAC + \angle BDC=\pi $ makes no sense, it implies $\angle BAC +\angle BCD=\pi$ which is not at all useful.I think the question should contain $\angle BAD + \angle BDC=\pi $ or$\angle BAC = \angle BDC $ to make quadrangle $ABCD$ a cyclic one.