# Tetrahedron

Geometry Level pending

Let $$ABCD$$ be a tetrahedron such that $$AB \perp AC \perp AD \perp AB$$ with integer side lengths $$AB,AC,AD,BC$$ and $$CD$$. Let $$E$$ be the midpoint of $$CD$$. If the volume of the tetrahedron $$ABCE$$ is 2016, how many distinct possible values of $$BD$$ are there?

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