# Mysterious point D

Geometry Level 4

Let ABC be a triangle. Let S be the circle through B tangent to CA at A and let T be the circle through C tangent to AB at A. The circles S and T intersect at A and D. Let E be the point where the line AD meets the circumcircle of $$\Delta ABC$$.

Find the ratio $$\frac{AD}{AE}$$.

If your answer is of the form $$\frac{ \sqrt a}{b}$$, where $$a$$ and $$b$$ are coprime integers, insert $$a + b$$ as your answer.

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