In the textbook I found this formula, and after a long time proving it,
And then it jumps to this...
My question is, is it correct that $$GH^2\ =\ 4R^2-4(a^2+b^2+c^2)???$$, shouldn't it be $4/9$ instead of just 4?
2026-05-14 03:45:11.1778730311
Possible Textbook Error/Geometry Euler line
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From the formulas shown above, just do a routine check that $GH^2 = (2OG)^2= 4OG^2= 4\left(\dfrac{OH}{3}\right)^2= \dfrac{4OH^2}{9}= \dfrac{4}{9}\left(9R^2-(a^2+b^2+c^2)\right)=4R^2- \dfrac{4(a^2+b^2+c^2)}{9}$ . So you are right, I think...