The point
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
is inside the convex quadrilateral
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
, such that
Prove that
![AB \cdot CM = BC \cdot MD](/media/m/4/c/0/4c0b01053a4ef888930fd02c0fc56a46.png)
and
%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 $BM \cdot AD = MA \cdot CD.$