Thread: Prove the following equation

Hi. How to prove that equation:



Additional informations:




and are heights of acute-angled triangle .

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

I would really appreciate any help.

First point is that most of the diagram is unnecessary.
If you don't need or
If you don't need or
Further, and serve no purpose.
All that you need is the triangle and the perpendiculars and

Using Pythagoras twice, with the triangles and



Now repeat that sequence using the triangles and

Having done that, add the resulting equation to the one that's just been derived.

Thank you very much. I've finally done that

Here are full calculations:

What equation would work for this problem?



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