Mixmatch

Algebra Level 1

If $$\color{blue}{a},\color{red}{b},$$ and $$\color{green}{c}$$ are distinct reals such that $\color{blue}{a}+\dfrac {1}{\color{red}{b}}=\color{red}{b}+\dfrac {1}{\color{green}{c}}=\color{green}{c}+\dfrac {1}{\color{blue}{a}},$ then find the value of $$|\color{blue}{a}\color{red}{b}\color{green}{c}|.$$

×