# Back To Back Right Triangles - 2

Geometry Level 3

In the above figure, $$ABD$$ and $$ACD$$ are integer-length, right-angled triangles with the right angle at $$D$$. If $$AD = 12$$ and $$BD$$ and $$DC$$ have different lengths, how many possible different lengths are there for $$BC$$?

Thanks to Brian for correcting my previous problem

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