# Cursed angle bisectors!

Geometry Level 5

Let there exist a right-angled triangle $$ABC$$, with $$\angle ABC = 90^{\circ}$$. Let $$CD$$ be the internal angle bisector of $$\angle ACB$$, with $$D$$ on $$AB$$ and let $$AE$$ be the internal angle bisector of $$\angle BAC$$, with $$E$$ on $$BC$$.

Let the length of $$AE$$ is $$9$$ and the length of $$CD$$ is $$8\sqrt{2}$$. If the length of $$AC$$ is $$a \sqrt{b}$$ where $$a$$ and $$b$$ are positive integers and $$b$$ is square-free, find the value of $$a+b$$.

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