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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