Question

a chord of a circle of radius 6cm subtends an angle of 60° at the center. find the area of minor segment​

Answer 1

Answer:

(6π-9√3)cm²

Step-by-step explanation:

The chord and the radius will form an equilateral triangle since the angle subtended by radius at centre is 60° and the other two angles are equal as these 2 angles are opposite to the two equal sides of the triangle.

Thus, Radii of the given circle is 6cm.

Ar(Minor segment) = Ar(Minor Sector) - Ar(Triangle)

=> Ar(Minor segment) = [(60°/360°) × π(6)²] - [(√3/4)×6²]

=> Ar(Minor segment) = 6π - 9√3

Hence, area of minor segment = (6π-9√3)cm² or 3(2π-3√3)cm²