Školjka

%V0 The point $M$ is inside the convex quadrilateral $ABCD$, such that $$MA = MC,\hspace{0,2cm}\widehat{AMB} = \widehat{MAD} + \widehat{MCD} \quad \textnormal{and} \quad \widehat{CMD} = \widehat{MCB} + \widehat{MAB}\text{.}$$ Prove that $AB \cdot CM = BC \cdot MD$ and $BM \cdot AD = MA \cdot CD.$