xnthic wrote:

Bunuel , how do you get \(\)"For equilateral triangle the radius of the circumscribed circle is R =side*\sqrt{3}/3, thus the area of that circle is πR2=π∗side23πR2=π∗side23.[/m]

you mind elaborating the steps in between? thank you !

Its an equilateral triangle, we can draw median/altitude from all the vertices which will meet at the center of the circle. That point is called centroid and it divides the length into 2:1 ratio.

So we know the length of median in an equilateral triangle is = \(\frac{Side}{2}\)*\sqrt{3}

Radius of the circle if you refer to the figure is the length OA which is 2 parts of the median:

= \(\frac{2}{3}\)*\(\frac{Side}{2}\)*\sqrt{3}

= \sqrt{3}*\(\frac{Side}{3}\)

HTH

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