# Length of Median?

Geometry Level 5

$$\triangle ABC$$ has an area of $$15\sqrt{3}$$ with $$\angle BAC =120^{\circ}$$ and $$\angle ACB < \angle ABC$$. The distance from $$A$$ to the centre of the circle inscribed in $$\triangle ABC$$ is $$2$$.

If the length of the median drawn from $$B$$ is $$\sqrt{ab}$$, where $$a$$ and $$b$$ are positive coprime integers and square-free, find $$a + b$$.

×