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A constellation is a patch of sky. Asking how far away it is is meaningless. You could ask how far away individual stars are, but there are a lot of stars in Cygnus at many vastly different distances.

Deneb, the brightest star in Cygnus, is a bit of a quandary; it's variable, making its distance difficult to measure. The generally accepted value is about 2600 light years, but the Hipparchos satellite measurement is about half that, at around 1500 light years.

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