The question from my textbook was "Give a complete proof that the largest triangle that can be inscribed in a circle is an equilateral triangle ", largest meaning that with the greatest area.(adsbygoogle = window.adsbygoogle || []).push({});

I found a proof that finds the area of the general triangle in terms of the angles, and through quite a bit of calculus trickery showed that it reached a maximum when all angles were equal to 60 degrees, ie Equilateral triangle, but my teacher said that there was a different, geometric based proof that didn't require calculus at all, though he could not produce it. This question came from a chapter of the textbook that was past basic Differentiation, but not yet up to the derivatives of trig functions, so there probably should be a more elementary proof right? If anyone has any ideas, please share !

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# Alternative Geometric Proof ideas?

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