Mahabir Singh Solutions for Chapter: Areas Related to Circles, Exercise 3: ACHIEVERS SECTION (HOTS)

In the given figure three circles of radius 2cm touch one another externally. These circles are circumscribed by a circle of radius $R \mathrm{cm}$, Find the area $(\mathrm{in} {\mathrm{cm}}^2)$ of the shaded region in terms of $\mathrm{\pi }$ and $\surd 3$).

Match the shaded region given in column-I with their areas in column-II 

Column I	Column II
(P)	$262.50 {\mathrm{cm}}^2$
(Q)	$271.04 {\mathrm{cm}}^2$
(R)	$427.14 {\mathrm{cm}}^2$

The circumcircle of $△ABC$ with $\angle A=60°$ has its centre at $O$ and radius equal to $2 \mathrm{cm}$ . Circle centered at $O$, touches the circumcircle and also $OB$ and $OC$. The radius of the smaller circle $(\mathrm{in} \mathrm{cm})$ is 

In the given figure, $ABC$ is a right-angled triangle, right –angled at $A$. Semi-circles are drawn on $AB, AC$ and $BC$ as diameters. Find the area of the shaded region.

In the figure, $ABCD$ is a square of side $10 \mathrm{cm}$. Find

(i) Area of inscribed circle

(ii) Area of circumscribed circle

(iii) Area of shaded region