Does this sort of triangle look familiar to you?

Geometry Level 3

The area of \(\Delta ABC\) is \(\varDelta = 6 \text{ unit}^2\) and the product of the length of its sides \(a,b,c\) is \(abc = 60\). If the radius of the incircle of this triangle is 1, then find the value of

\[\dfrac 1a + \dfrac 1b + \dfrac 1c.\]

Give your answer to 3 decimal places.

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