CEMC Euclid, 1998

Geometry Difficulty 2.0 Junior Prove it Canada

In the diagram, $DC$ is a diameter of the larger circle centred at $A$ , and $AC$ is a diameter of the smaller circle centred at $B$ . If $DE$ is tangent to the smaller circle at $F$ , and $DC=12$ , determine the length of $DE$ .

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