# Circumcircle

Level pending

In acute $$\triangle ABC$$, $$\angle BAC= \tan^{-1} \left ( \dfrac{3 \sqrt{5}}{7} \right )$$ and $$AC= \dfrac{2}{3}AB$$. A point $$D$$ is chosen on $$AC$$ extended such that $$AD= AB$$. The circumcircle of $$\triangle CDB$$ intersects $$AB$$ at two points: $$E$$ and $$B$$. If $$\dfrac{AE}{AB}= \dfrac{a}{b}$$ for some coprime positive integers $$a, b$$, find $$a+b+3$$.

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