Connection and relation
关 (guān) in words like 关于 and 关系 signals a link or connection between things.
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关has 2 distinct senses for the same pronunciation

关 (guān) in words like 关于 and 关系 signals a link or connection between things.
about
be related to; be bound up with; correlation
关 (guān) in words like 关闭 and 海关 refers to shutting something or controlling access.
to turn off (a machine or device)
关 (guān) in words like 关心 and 关注 expresses caring for or paying attention to someone or something.
no problem
Mom cares about me very much.
We have a good working relationship.
Parents always care about their children's growth.
Please close the door.
This matter is unrelated to my work.
Explore characters by relationship
Characters from the same exam level.
Characters pronounced "guan".
Characters with radical "丷".