Calculate the radius of a circle around an equilateral triangle if its side is 9 √3.

univerkov | June 22, 2021 | education

Since triangle ABC is isosceles, all of its internal angles are equal to 60.

Then Savs = AB * AC * Sin60 / 2 = 9 * √3 * 9 * √3 * √3 / 4 = 243 * √3 / 4 cm2.

Also Savs = AB * CH / 2.

CH = 2 * Savs / AB = (243 * √3 / 2) / (9 * √3) = 27/2 cm.

Point O, the center of the circle and the point of intersection of the medians, then R = OC = CH * 2/3 = (27/2) * (2/3) = 9 cm.

Answer: The radius of the circumscribed circle is 9 cm.

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