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> Math Olympiad Question:
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> If $a^2+b^{2\ }=\ c^2$ what is the value of $a^2-b^{2\ }$ in terms of $c$?
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I was solving some problems of the Indian National Mathematics Olympiad and I found this problem to be very intriguing. At first look it looks pretty straight forward but this problem requires the solution to be in terms of $c$ only, meaning that if you have the value of c, put that in your solution and you should get the same value as $a^2-b^{2\ }$.

I tried simple algebra, trigonometry, geometry and pattern recognition but none of these methods were quite successful and could give a reasonable proof + solution.

My question is how to find the solution and prove this question? Is it possible to use Geometry and solve?

EDIT -
Sorry my bad, I think $a>b$ and $a$ and $b$ are integer values as in the starting of the exam it's written that all values will be integer and non-negative.

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> FINAL EDIT:
> I think this question has been misprinted. Sorry for the inconvenience.
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