# Nasty Triangles 3

Geometry Level 5

Given a circle and $$\triangle ABC$$, the circle passes through $$A$$ and $$B$$ and intersects $$\triangle ABC$$ at point $$D$$ and $$E$$. Extend $$AB$$ and $$DE$$ so that they intersect at point $$F$$, connect line $$CF$$.

If $$AB=3$$, $$AD=1$$, $$DC=2$$, and $$\frac{AE}{BD}=\frac{\sqrt5}{2}$$, find the length of $$CF$$.

Also try Nasty Triangles 4.

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