Minimizing a Geometrical Expression!

Geometry Level 4

\[\large{\Omega = \left(1+ \dfrac{r_a}{R_a} \right)\left(1+ \dfrac{r_b}{R_b} \right)\left(1+ \dfrac{r_c}{R_c} \right)}\]

Let \(P\) be a point inside an equilateral triangle \(ABC\), and let \(R_a,R_b,R_c\) and \(r_a, r_b, r_c\) denote the distances of \(P\) from the vertices and edges, respectively, of the triangle. Find the minimum value of \(\Omega\).

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