Enigmatic person is cross after panic outside hospital (6)

I believe the answer is:

sphinx

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'enigmatic person' is the definition.
(creature posing riddles in mythology)

I don't understand the remainder of the clue.

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(Other definitions for sphinx that I've seen before include "Stone figure by the pyramids at Giza" , "Enigmatic person; Egyptian statue" , "Egyptian atatue with lion's body and man's head" , "Ancient riddler" , "Monster - Egyptian statue" .)

I've seen this clue in The Guardian.

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