In the figure,ABC is an equilateral triangle inscribed in a circle of radius 4cm with centre O.Find the area of the Shaded region.


We know that median is divided into ratio 2: 1 by the centroid.Hence, AO: OD = 2: 1. Using AO = 4 cm, we get OD = 2 cm.

Also, since its an equilateral triangle, median AD will also act as altitude from A on BC.Now in right triangle ODC

Subsequently BC = 2DC =
Area of triangle ABC

Area of triangle AOC (shaded in green) = Area of triangle BOA = Area of triangle BOC =(Area of triangle ABC)
Area of each segment (shaded in red) =(Area of circle -Area of Traingle ABC)


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