# Combinatorics in Geometry

In triangle $$\Delta ABC$$, $$\overline {AB} = 12$$, and $$\overline {AC} = 5$$. Given that $$\overline{BC}$$ is chosen uniformly in the interval of permissible values such that $$\Delta ABC$$ is a non-degenerate triangle .

The probability that $$\Delta ABC$$ is an acute triangle can be expressed in the form $$\large \frac{a - \sqrt{b}}{c}$$ where $$a$$, $$b$$ and $$c$$ are coprime positive integers. Determine $$a + b + c$$.

Follow up question: Could you generalize this probability for any triangle with two known sides $$x$$, and $$y$$?

×