Cyclic Means

Algebra Level 2

The mean of the two numbers \(a\) and \(b\) is \(c\).
The mean of the two numbers \(b\) and \(c\) is \(a\).
The mean of the two numbers \(c\) and \(a\) is \(b\).

Is it possible for all the statements above to be fulfilled at the same time for distinct numbers \(a,b\) and \(c\)?

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