Teach girl, perplexed by how apathetic she is (9)

I believe the answer is:

lethargic

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'how apathetic she is' is the definition.
I can't tell whether this defines the answer.

'teach girl perplexed' is the wordplay.
'perplexed' indicates anagramming the letters.
'teach'+'girl'='teachgirl'
'teachgirl' with letters rearranged gives 'LETHARGIC'.

'by' is the link.

Can you help me to learn more?

(Other definitions for lethargic that I've seen before include "Lacking in energy or vitality" , "Lacking energy/enthusiasm" , "somewhat slow" , "Unenergetic" , "Sluggish and apathetic" .)

I've seen this clue in The Irish Times.

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