This is the 13936th most frequent Russian word.
обращаясь
"Обращаясь" - "addressing" or "turning to" (when acting or referring to someone/something).
Here, 'обращаясь' is used as a gerund (деепричастие) indicating the simultaneous action of addressing the audience while being convincing.
Обращаясь к публике, он постарался быть убедительным.
Addressing the audience, he tried to be persuasive.
In this example, 'обращаясь' is a gerund showing the action of seeking help happening concurrently with her hoping to find support.
Обращаясь за помощью, она надеялась найти поддержку.
Reaching out for help, she hoped to find support.
Here, 'обращаясь' indicates the simultaneous action of the children interacting with each other while observing the clown.