Question

From a metal sheet which is in the shape of a circle a biggest square with 10 cm as side was taken. Then the radius of the circle is (in cms)

 A) 5√2 

B) 10√2 

C) 5

D) 7.5

Answer 1

Correct option is (A) 5√2

Let ABCD is a square of side 10 cm are lying inside the circle of radius r.

\(\because\angle ABC=90^\circ\)      \((\because\) Angle in a square)

\(\therefore\) AC is a diameter    \((\because\) Angle in a semicircle is \(90^\circ)\)

\(\therefore AC=\sqrt{AB^2+BC^2}=\sqrt{10^2+10^2}\)

\(=\sqrt{100+100}=10\sqrt2\,cm\)

\(\therefore\) Radius \(=\frac{Diameter}2\)

\(=\frac{AC}2=\frac{10\sqrt2}2=5\sqrt2\,cm\)

Answer 2

Correct option is  B) 10√2