Answer :


Given: Radius of the circle = 21 cm and angle subtended by the arc = 60°


(i) We know that the length of the arc


Length of BDC


(ii) We know that the area of the minor sector


Area of ABDC


Area of ABDC = 231cm2


(iii) Area of the segment BDC = area of sector ABDC – area of triangle ABC


In ∆ABC,


A = 60°, AB = AC = 21 cm {radius of the circle}


ABC = ACB {angles opposite to equal sides are equal}


By the angle sum property of the triangle,


ABC + ACB + A = 180°


2ABC = 180° - 60°


ABC = 60°


Hence, ∆ABC is an equilateral triangle.


Area of a equilateral trianglewhere a is the side of it.


Area of ∆ABC


Area of ∆ABC = 190.95cm2


Area of the segment BDC = area of sector ABDC – area of triangle ABC


Area of the segment BDC = 231 – 190.95


Area of the segment BDC = 40.05cm2


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