Prove that; $a^{2} + b^{2} + c^{2} = 8 R^{2}$ . where $R$ is the circum radius.

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Solution

We have prove that,
$a^{2} + b^{2} + c^{2} = 8 R^{2}$ .....(right angle $Δ$ prop)
where $R$ is circum radius ,
Now, we know that ,
$a^{2} + b^{2} + c^{2} = 2 c^{2}$
And $R$ is half of $c$
$∴ 8 R^{2} = a^{2} + b^{2} + c^{2}$

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