Hi. How to prove that equation:

$\displaystyle |AB|^{2} = |QA| * |AE| + |NB| * |BD|$

Additional informations:

$\displaystyle |BN| = |BC|$

$\displaystyle |AQ| = |AC|$

$\displaystyle |AD|$ and $\displaystyle |BD|$ are heights of acute-angled triangle $\displaystyle ABC$.

Illustration: http://i.imgur.com/9O8Bm.jpg

I would really appreciate any help.