Question

In the given figure, a square $OACE$ is inscribed in a quadrant $OBCD$. If $OA=8\sqrt{2}\text{cm}$, then the radius of the circle is

• A. $8\sqrt{2}\text{cm}$
• B. $8\text{cm}$
• C. $16\sqrt{2}\text{cm}$
• D. $16\text{cm}$

Answer 1

The correct option is D $16\text{cm}$


$OACE$ is a square such that $OA$ is $8\sqrt{2}\text{cm}$.
Now, $OC$ is the diagonal of square.
$\Rightarrow OC=\sqrt{2}\times$ Side
$\Rightarrow OC=\sqrt{2}\times OA$
$\Rightarrow OC=\sqrt{2}\times 8\sqrt{2}=16\text{cm}$

Since, $OBCD$ is a quadrant of circle with radius $OB$ and $OB=OC=OD$
Thus, the radius of the circle is $16\text{cm}$

Hence, the correct answer is option d.