# You could beat the world

Geometry Level pending

$$ABC$$ is a right triangle with $$\angle A = 90^\circ$$. Let a circle tangent to $$AB$$ at $$A$$ and tangent to $$BC$$ to some point $$D$$. Suppose the circle intersects $$AC$$ again at $$E$$ and the $$CE = 3$$ cm, $$CD = 6$$ cm, what is $$BD$$?

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