# It's an integer right?

Geometry Level 5

The sides of a $$\triangle ABC$$ are the tangents to the parabola $$y^2 = 4ax.$$

Let $$D,E,F$$ be the points of contact of side $$BC,CA$$ and $$AB$$ respectively.

If lines $$AD,BE,CF$$ are concurrent at the focus of the parabola.

Let the $$\angle ABC$$ of $$\triangle ABC$$ be $$\dfrac{\pi}{\alpha}$$.

Find the value of $$\alpha^\alpha-8$$.

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