On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. Find the covered area of the design.
Join AO and extend it to D on BC.
Radius of the circle, r = 42 cm
∠OCD=30ocos 30o=DCOC⇒√2=DC42⇒DC=21√⇒BC=2×DC=2×21√=72.66cmsin 30o=ODOC⇒12=OD42⇒OD=21 cm
Now, AD=AO+OD=42+21=63 cm
Area of the shaded region = Area of circle – Area of triangle ABC