Question

a square ABCD is inscribed in a circle of radius R find the area of the square

Answer 1

check the solution.....

Answer 2

Answer:  The area of the square is 2R².

Step-by-step explanation: AS given in the question, we have drawn a square ABCD inscribed in a circle with centre 'O' and radius 'R' units.

We are given to find the area of the inscribed square.

Since all the sides of a square are equal, so the diagonal of the square will definitely pass through the centre 'O' of the circle.

So, the diagonals will be the diameters of the circle.

Therefore, length of the diagonal BD will be

$BD=R+R=2R.$

As every angle of the square ABCD is a right-angle, so from right-angled triangle BCD, we have

$BD^2=BC^2+CD^2~~~\textup{(Pythagoras Theorem)}\\\\\Rightarrow (2R)^2=BC^2+BC^2\\\\\Rightarrow 4R^2=2BD^2\\\\\Rightarrow BD^2=2R^2.$

Since the area of a square is (side)² and BD is one of the sides, so the area is 2R².