Question

In the adjoining figure O is the centre of the circle with radius 'r' AB, CD and EF are the diameters of the circle. $\angle OAF=\angle OCB={60}^{\circ }$. What is the area of the shaded region?

• A. $\frac{r^2}{2}(\pi -\frac{3\sqrt{3}}{2})$
• B. $\frac{r^2}{2}(\pi -\frac{3\sqrt{3}}{4})$
• C. $\frac{r^2}{3}(\pi -\frac{2\sqrt{3}}{3})$
• D. $Datainsufficient$

Answer 1

The correct option is A $\frac{r^2}{2}(\pi -\frac{3\sqrt{3}}{2})$

Notice that all the given triangles are equilateral
Area of shaded region $=3[\pi r^2\frac{60}{360}-\frac{\sqrt{3}}{4}\times r^2]=\frac{r^2}{2}[\pi -\frac{3\sqrt{3}}{2}]$