<Tri-2023-2042>, hint

By ceva concurrence$\iff \frac{BE}{EC}=\frac{BD}{DA}\iff DE//AC$
$\iff ECMD$ is an isosceles trapetium$\iff EC=DM$
$\iff CE=CM$.
The last equivalence is because $M$ is the center of the semicircumference $(ADC)$

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