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"Triangle with largest area is an equilateral triangle."

Is this a theorem or smth? It makes sense, but how do you know?

I remember reading it somewhere, but cannot recollect where. Of course, I may be wrong.

Just guessing on this (based on sketches) - possibly the largest triangle that can be inscribed in a circle is equilateral, but if one vertex is the center of the circle, rather than on the circumference, then I agree it has to be a right triangle. So the area would be 1/2.