# Isosceles triangle pt.2

Geometry Level 4

$$ABC$$ is an isosceles triangle with $$AC=BC$$ and has an angle $$ACB=108^\circ$$.
If the ratio of $$\dfrac{AB}{BC}$$ can be represented as $$\dfrac{a+\sqrt{b}}{c}$$, where $$a,b$$ and $$c$$ positive integers with $$b$$ square-free, find $$a+b+c$$.

Bonus: Try to do this without trigonometry.

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