a. Ta có:
$\angle BDM=\angle BFM \Rightarrow BDMF$ nội tiếp.
$\angle CDM=\angle CEM \Rightarrow CDME$ nội tiếp.
b. Ta có:
$\angle DMF=180^o-\angle DBF=180^o-\angle DCE=\angle DME$
c. Ta có:
$\angle MDE=\angle MCE=\angle CBM=\angle DFM$
mà $\angle DME=\angle DMF$
$\Rightarrow \Delta DME\sim\Delta FMD \Rightarrow \dfrac{MD}{MF}=\dfrac{ME}{MD} \Rightarrow MD^2=ME.MF$