# The chord contracts the arc at 60 degrees. The length of the arc is 2 p.

**The chord contracts the arc at 60 degrees. The length of the arc is 2 p. Find the length of the chord and the area of the corresponding sector.**

To the edges of the chord, points A and B, draw the radii of the circle OA and OB.

The degree measure of the arc AB, according to the condition, is 60, then the central angle AOB is equal to the degree measure of the arc AB, the angle AOB = 60.

Since in the triangle AOB, AO = OB = R, and the angle AOB = 60, then triangle AOB is isosceles, and OA = OB = R.

We define the radius of the circle through the length of the chord AB.

L = n * R * 60/180 = 2 * n.

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

Since the triangle AOB is isosceles, then AB = R = 6 cm.

Let’s determine the area of the AOB sector.

Ssec = n * R2 * 60/360 = n * 36 * 60/360 = 6 * n cm2.

Answer: The length of the chord is 6 cm, the area of the sector is 6 * π cm2.