# 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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