# I begin

Geometry Level 4

$\begin{cases} a^{2}+b^{2}+c^{2}=50 \\ a^{3}+b^{3}+c^{3}=216 \\ ab+bc+ca=47 \end{cases}$

For $$\triangle ABC$$ with sides $$a,b$$ and $$c$$, let $$R$$ and $$r$$ denote the radius of circumcircle and incircle of $$\triangle ABC$$. If the values of $$a,b$$ and $$c$$ satisfy the system of equations above, find the value of $$R \times r$$.

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