Question

In the given figure, $Q P R$ is quadra circle and $A B C D$ is a square, whose side is $\sqrt{10} cm$. If $A$ and $B$ are equidistant from the centre $O$, then find the radius of the circle.

• A. 2
• B. 3
• C. 5
• D. 7

Answer 1

Answer: (C)

Given, $B C=\sqrt{10} cm$

In $\triangle B D C$,
$B D^2=B C^2+C D^2 $
$B D^2=10+10 $
$B D^2=20$
$B D=\sqrt{20} cm $
$\text { In } \triangle O A B, O B^2+O A^2=A B^2$
$2\left(O B^2\right)=10(\because O B=O A) $
$O B^2=5$
$O B=\sqrt{5} cm .$
In $\triangle O B D$,
$O D^2=O B^2+B D^2$
$O D^2=5+20 $
$O D=\sqrt{25}$
$O D=5 cm$
$\therefore$ Required radius is $5 \,cm$.