# Dealing with centres

Geometry Level 4

In a triangle $$\Delta \text{ABC}$$ , if $$b=2\text{ cm}, c=\sqrt{3}\text{ cm}$$ and $$\angle A = \dfrac{\pi}{6}$$, then the distance between its circumcenter and incenter could be represented as $$\sqrt{m - \sqrt{n}}$$.

Then find $$m+n$$.

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