Question

In the adjoining figure, a smaller circle touches a larger circle internally and passes through the centre $O$ of the latter. If the area of the smaller circle is $200c{m}^2$ then the area of the larger circle in $c{m}^2$ is :

• A. $200c{m}^2$
• B. $400c{m}^2$
• C. $600c{m}^2$
• D. $800c{m}^2$

Answer 1

Answer: (D)

$800c{m}^2$

Area of smaller circle $=\pi r^2=\frac{22}{7}\ast r^2=200$
$⟹r^2=\frac{700}{11}orr=10\sqrt{\frac{7}{11}}$
The radius of the big circle is diameter of small circle.
Area of big circle $=\pi R^2=\frac{22}{7}\ast R^2=\frac{22}{7}\ast 20\sqrt{\frac{7}{11}}\ast 20\sqrt{\frac{7}{11}}=800{cm}^2$