A regular triangle is inscribed in a circle with a radius of 36 cm, find its perimeter.

univerkov | September 9, 2021 | education

The ABC triangle is correct, AB = BC = AC. Angle BAC = BCA = 60. The bisectors OA and OS intersect at the center of the circle O.

Then triangle AOC is isosceles, OA = OC = R, angle AOC = OCA = 60/2 = 30, and angle AOC = (180 – 30 – 30) = 120.

By the cosine theorem, we define the length of the AC side.

AC ^ 2 = R ^ 2 + R ^ 2 – 2 * R * R * Cos120.

AC ^ 2 = 2 * R ^ 2 – 2 * R ^ 2 * (-1/2) = 2 * R ^ 2 + R ^ 2 = 3 * R ^ 2.

AC = R * √3 cm.

Then Ravs = 3 * AC = 3 * R * √3 cm = 108 * √3 cm.

Answer: The perimeter of the triangle is 108 * √3 cm.

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