In a circle, the degree measure of the arc AB is 60 degrees. Prove that the chord AB is a side of a regular

In a circle, the degree measure of the arc AB is 60 degrees. Prove that the chord AB is a side of a regular n-gon inscribed in a circle, and its length is equal to the radius of this circle.

Let’s draw the radii of the circle OA and OB. Since the degree measure of the arc AB is equal to 60, the central angle AOB is also equal to 60.

Triangle AOB is isosceles, since OA = OB = R, and since one of the acute angles of the triangle is 60, then triangle AOB is equilateral. AB = OB = OA = R.

The central angle AOB is one sixth of the degree measure of the circle 360/60 = 6, and therefore a regular hexagon is inscribed in the circle, the side of which is equal to the radius of the circle, which was required to prove.