The chord of the circle is 6 and contracts the arc of 60 degrees. Find the length of the arc and the area

The chord of the circle is 6 and contracts the arc of 60 degrees. Find the length of the arc and the area of the corresponding sector.

Let’s draw the radii of the circle OB and OA, then the triangle AOB is isosceles. Since the chord AB contracts the arc at 60, the central angle resting on this chord is also 60. Then the triangle AOB is isosceles and one of the angles is 60, which means this triangle is equilateral OA = OB = AB = R = 6 cm.

Let us determine the length of the arc AB.

L = n * R * α / 180, where α is the arc angle in degrees.

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

Let’s define the area of the sector.

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

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