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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