a/ Ta có :
\(+,AD+DB=AB\)
+) \(AE+EN=AC\)
Mà \(AB=AC,AD=AE\)
\(\Leftrightarrow DB=EN\)
Xét \(\Delta DBM;\Delta ECN\) có :
\(\left\{{}\begin{matrix}\widehat{DMB}=\widehat{ENC}=90^0\\DB=EC\\\widehat{DBM}=\widehat{ENC}\end{matrix}\right.\)
\(\Leftrightarrow\Delta DMB=\Delta ENC\left(ch-gn\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}BM=NC\\MD=NE\end{matrix}\right.\)
b/ \(\Delta BDE=\Delta DEC\left(c-g-c\right)\)
\(\Leftrightarrow BE=DC\)
Xét \(\Delta DMC\) có : \(\widehat{DMC}=90^0\)
\(\Leftrightarrow DM< DC=BE\)
\(\Delta DME=\Delta NEM\)
\(\Leftrightarrow DE=MN\)
Xét \(\Delta BEN\) có : \(\widehat{BNE}=90^0\)
\(\Leftrightarrow BN< BE\)
Xét \(\Delta DMC\) có ; \(\widehat{DMC}=90^0\)
\(\Leftrightarrow MC< DC\)
Mà \(BE=BC\)
\(\Leftrightarrow BN+MC=2.BE\)
Ta có :
\(MN+MB+MC< 2.BE\)
\(\Leftrightarrow DE+BC< 2.BE\left(đpcm\right)\)
