Y by
Let
be a triangle for which there exists an interior point
such that
. Let the lines
and
meet the sides
and
at
and
respectively. Prove that
![\[ \sqrt{AB\cdot AC}\geq2DE. \]](//latex.artofproblemsolving.com/f/b/e/fbe0ef3fd6366c4ef411020fc5a3f6f337f18fe0.png)









![\[ \sqrt{AB\cdot AC}\geq2DE. \]](http://latex.artofproblemsolving.com/f/b/e/fbe0ef3fd6366c4ef411020fc5a3f6f337f18fe0.png)
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