A chord of a circle equal to m subtracts an arc of 120 °. Find the radius of the circle.

Since the chord AB contracts the arc at 120, the central angle resting on this arc is also equal to 120.

From point O, the center of the circle, draw the radii of the circle OA and OB.

Since ОА = ОВ = R, the triangle AOB is isosceles. Let’s draw the height OH to the base AB of the triangle ABC. In an isosceles triangle, the height is also the bisector and median of the triangle. Then AH = BH = m / 2, and the angle AOH = BOH = 120/2 = 60.

In a right-angled triangle АHО SinАН = АH / ОА.

OA = AH / Sin60.

ОА = (m / 2) / (√3 / 2) = m / √3 cm.