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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