# A Surprising Symmetry

Geometry Level 4

$\large \dfrac {b-c}{\sin (\frac {\angle B-\angle C}{2})}$

In acute $$\triangle ABC$$, the side lengths across from angles $$A,B,C$$ are denoted $$a,b,c$$ respectively. It is given that $$a=10$$ and the circumradius of $$\triangle ABC$$ is 13.

If the absolute value of the expression above can be written as $$\sqrt {n}$$, then find $$n$$.

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