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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.

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