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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