Points A and B are selected on the circle, so the large arc AB = 240 degrees.

Points A and B are selected on the circle, so the large arc AB = 240 degrees. Find the length of the chord AB (arc) if the radius of the circle is 10 m.

The large arc AB is equal to 240, then the smaller arc is: 360 – 240 = 120 (degrees). The central angle resting on the smaller arc AB is 120 degrees, because the degree measure of the central angle is equal to the degree measure of the arc on which it rests.
The chord length is found by the formula:
l = 2Rsin (α / 2),
where R is the radius of the circle, α is the central angle based on the chord AB.
l = 2 * 10 * sin (120/2) = 20 * sin60 = 20 * (√3 / 2) = 20√3 / 2 = 10√3 (m).
Answer: l = 10√3 m.