Question 13
G7 (ARM). The point $M$ inside the convex quadrilateral $ABCD$ is such that
$$MA=MC,\quad\angle AMB=\angle MAD+\angle MCD,\quad\angle CMD=\angle MCB+\angle MAB.$$
Prove that $AB\cdot CM=BC\cdot MD$ and $BM\cdot AD=MA\cdot CD$.
$$MA=MC,\quad\angle AMB=\angle MAD+\angle MCD,\quad\angle CMD=\angle MCB+\angle MAB.$$
Prove that $AB\cdot CM=BC\cdot MD$ and $BM\cdot AD=MA\cdot CD$.