Question

A chord of a circle of radius 30 cm makes an angle of 60° at the centre of the circle. Find the areas of the minor major segments.

Answer 1

Let the chord be AB. The ends of the chord are connected to the centre of the circle O to give the triangle OAB.

OAB is an isosceles triangle. The angle at the centre is 60°

Area of the triangle `=1/2(30)^2  sin 60^circ = 450xxsqrt(3)/2 = 389.25  "cm"^2`

Area of the sector OACBO` =60/360xxpixx30xx30 = 150pi = 471  "cm"^2`

Area of the minor segment = Area of the sector - Area of the minor segment 

= (π × 30 × 30)  - 81.29

= 2744.71 cm²