Question

In the given figure, $QPR$ is quadra circle and $ABCD$ 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, $BC=\sqrt{10}cm$

In $△BDC$,
$B{D}^2=B{C}^2+C{D}^2$
$B{D}^2=10+10$
$B{D}^2=20$
$BD=\sqrt{20}cm$
$\text{ In }△OAB,O{B}^2+O{A}^2=A{B}^2$
$2\left(O{B}^2\right)=10(\because OB=OA)$
$O{B}^2=5$
$OB=\sqrt{5}cm.$
In $△OBD$,
$O{D}^2=O{B}^2+B{D}^2$
$O{D}^2=5+20$
$OD=\sqrt{25}$
$OD=5cm$
$\therefore$ Required radius is $5cm$.