A chord of a 6 cm circle contracts an arc of 60 degrees. Find the length of the arc, the area of the corresponding sector.

From point O, the center of the circle, draw segments OA and OB equal to the radius of the circle.

The central angle AOB is equal to the degree measure of the arc that contracts the chord AB. Angle AOB = 60. Since OA = OB, and one of the angles of the triangle is 60, then triangle AOB is equilateral, AO = BO = AB = R = 6 cm.

Let us determine the length of the arc AB by the formula: L = n * R * α / 180, where R is the radius of the circle, and α is the angle between the radii.

L = n * 6 * 60/180 = 2 * n cm.

Let us determine the area of the OAB sector.

Soav = n * R2 * α / 360 = n * 36 * 60/360 = 6 * n cm2.

Answer: The length of the arc is 2 * n cm, the area of the sector is 6 * n cm2.