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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