Question

The area of a square that can be inscribed in a circle of radius r is

• A. $r^2$
• B. $2r^2$
• C. $4r^2$
• D. $\pi r^2$

Answer 1

The correct option is B $2r^2$

Given radius of circle is r

Then area of circle=$\pi r^2$

Since two opposing corners of the square touch the circle, that diagonal in the square is equivalent to the diameter (2r) of the circle.

Now to find one side of the square we will set up Pythagoras theorem:

$a^2+b^2=c^2$

Since it is a square a=b which means all the sides are same

$\therefore 2a^2=c^2$

We know c, which is 2r, the diagonal.

$\therefore 2a^2=(2r{)}^2\Rightarrow 2a^2=4r^2\Rightarrow a^2=2r^2$

We can leave it as $a^2$ since a is one side of the square and $a^2$ would be the area of the square.

So the area of the square =$2r^2$