Awesome Geometry!

Geometry Level 5

The ratios of the lengths of the sides \(BC\) and \(AC\) of \(\triangle ABC\) to the radius of its circumscribed circle are equal to 2 and 1.5 respectively.

Find the ratio of the lengths of the bisectors of the interior angles \(B\) and \(C\) .

If the answer can be expressed in the form \(\dfrac{a\sqrt{b} - a\sqrt{c}}{d}\), where \(a\), \(b\), \(c\) and \(d\) are positive integers with \(a\) and \(b\) being square free, find \((a+b) - (c+d)\).

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