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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