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in Areas Related To Circles by (65.5k points)

In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design.

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(i) Radius of the circle r = 32 cm. 

∴ Area of the circle = πr2

\(\frac{22}{7}\) x (32)2

\(\frac{22}{7}\) x 1024

= 32118.28 sq.cm.

(ii) ∠BAC = 60° 

∴ ∠BOC = 120° (∵ Angle at the centre is double than the angle in the circumference). 

Now, in ∆OBC, BC ⊥ OD, 

∠BOD = ∠COD = 60°

∴ ∆ABC is an equilateral triangle. 

Each side of this triangle, 

a= 2 × 16√3 = 32√3cm

Area of equilateral triangle, ∆ABC :

(iii) Area of shaded region : 

= Area of circle – Area of an equilateral ∆le 

= 3218.28 – 1328.64 

= 1889.6 sq.cm.

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