The chord of the circle is 9 m. It contracts the arc at 60 degrees. Find the length of the arc

The chord of the circle is 9 m. It contracts the arc at 60 degrees. Find the length of the arc and the area of the corresponding sector.

The chord AB contracts the arc AB, the degree measure of which is 60, then the central angle AOB is equal to the degree measure of the arc on which it rests. Angle AOB = 60.

The AOB triangle is isosceles, since ОА = ОВ = R, and since one of its angles is 60, the AOB triangle is equilateral, ОА = ОВ = AB = R = 9 m.

Let us determine the length of the smaller arc AB.

L = π * R * 60/180 = π * 9 * 60/180 = 3 * π m.

Let us determine the area of the OAB sector.

Ssec = π * R2 * 60/360 = π * 81 * 60/360 = 13.5 * π m2.

Answer: The length of the arc is 3 * π m, the area of the sector is 13.5 * π m2.