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  • In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (iii) area of the segment formed by the corresponding chord

5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:

  (iii) area of the segment formed by the corresponding chord

Answers (1)

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For area of segment we need to subtract area of the triangle attached with the area of arc.

Thus consider the triangle :-

It is given that angle of arc is 60o, or we can say that all angles are 60o (since two sides are equal). Hence it is an equilateral triangle.  

Area of triangle is :- 

                                         \\=\ \frac{\sqrt{3}}{4}\times a^2\\\\\\=\ \frac{\sqrt{3}}{4}\times 21^2\\\\=\ \frac{441\sqrt{3}}{4}\ cm^2

Hence the area of segment is :-  

                                           =\ \left (231\ -\ \frac{441\sqrt{3}}{4} \right )\ cm^2                             

Posted by

Devendra Khairwa

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