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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.
Solution
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
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