The chord of the circle is equal to a and contracts the arc at 60. Find: a) the length of the arc;

The chord of the circle is equal to a and contracts the arc at 60. Find: a) the length of the arc; b) the area of the sector bounded by this arc and two radii.

From point O, the center of the circle, draw the radii OA and OB.

In an isosceles triangle OA = OB = R, one of the inner angles is 60, then the triangle AOB is equilateral, OA = OB = AB = R = a cm.

Let us determine the length of the arc AB.

Lav = π * R * 60/180 = π * a * 60/180 = π * a / 3 cm.

Let us determine the area of the OAB sector.

Soav = π * R ^ 2 * 60/360 = π * a ^ 2/6 cm2.

Answer: The length of the arc is π * a / 3 cm, the area of the sector is π * a ^ 2/6 cm2.