question_answer

The circumference of a circle is 100 cm. What is the side of the largest square inscribed in the circle?

A)  \[\frac{100\sqrt{2}}{\pi }cm\]                      

B)  \[\frac{50\sqrt{2}}{\pi }cm\]

C)  \[\frac{100}{\pi }cm\]                       

D)  \[50\sqrt{2}\,cm\]

Correct Answer: B

Solution :

    Let r be the radius of the circle in centimeter. Then its circumference\[=2\pi r=100\] \[\therefore \] Diameter\[=2r=\frac{100}{\pi }\] The length of the largest diagonal of the square = diameter of the circle\[=2r=\frac{100}{\pi }cm\] \[\therefore \] Side of square \[=\frac{1}{\sqrt{2}}\times \] Largest diagonal \[=\frac{1}{\sqrt{2}}\times \frac{100}{\pi }=\frac{50\sqrt{2}}{\pi }cm.\]