What is the arc length of the circumscribed circle of a triangle? As the height of three sides of a triangle, the intersection point is the center. Because the side length is 6, the radius of the circumscribed circle is 2, and the center of the circle is the center of the triangle. Then the circumference of the circle will be known. If it is a triangle inscribed with a circle, the center of the circle is still the center of the triangle, but the radius is root number 3, and the circumference of the circle will be known.

Equilateral triangle > > The center o is in the center of the triangle, and the radius =OA=OB=OC.

OA bisects BAC, connects BO and extends AC to point D.

Because O is the center of a regular triangle, BD is the height on the side of AC, and AC is equally divided, then AOD is a right triangle with an angle of 30 degrees.

R=OC= 1/2AC/ (√3/2)=2√3，

The arc length of the three segments = the circumference of the circumscribed circle of an equilateral triangle ABC =2πR=4√3π.