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解:$\because DE$是$\triangle ABC$的边$AC$的垂直平分线,
$\therefore AE=CE$.
$\therefore \triangle EBC$的周长为$BC+BE+EC=BC+BE+AE=8+10=18$.
解:$\because DE$是$\triangle ABC$的边$AC$的垂直平分线,
$\therefore AE=CE$.
$\therefore \triangle EBC$的周长为$BC+BE+EC=BC+BE+AE=8+10=18$.