# From where do I start the chase?

Geometry Level 5

Consider an isosceles $$\Delta ABC$$ with points $$E_{1}, E_{3}, E_{5}, \cdots E_{99}$$ on side $$AC$$ and points $$E_{2}, E_{4}, E_{8}, \cdots E_{100}$$ on side $$AB$$ such that $$AE_{1} = E_{1}E_{2} = E_{2}E_{3} = \cdots = E_{99}E_{100} = E_{100}C = BC$$. Now, $$\angle BAC$$ , in degrees, is of the form $$\dfrac{x}{y}$$ where $$x$$ and $$y$$ are coprime natural numbers. Find $$x+y-72$$.

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