# Inspired by Hung Woei Neoh

Geometry Level 4

$x^3-24x^2+180x-420=0$

A $$\triangle ABC$$ has side lengths $$a$$, $$b$$ and $$c$$, which are also the roots of the equation above. If $$a\cos A+b\cos B+c\cos C=\dfrac{p}{q}$$, where $$p$$ and $$q$$ are coprime positive integers. Find $$p+q+10$$.

×