SED - Print - Print paragraph if it contains string1 or string 2 or string3

Print paragraph if it contains AAA or BBB or CCC.

sed -e '/./{H;$!d;}' -e 'x;/AAA/b' -e '/BBB/b' -e '/CCC/b' -e d
gsed '/./{H;$!d;};x;/AAA\|BBB\|CCC/b;d'         # GNU sed only