Question

A square is inscribed in a circle such that each corner touches the circle.

Answer 1

Answer:

A(r) = √2 * r

A(r) Domain is   R { r ;  r > 0}

Step-by-step explanation:

Diagonals of a square intercept each other in a 90° angle. The four triangles resulting from diagonal interception are equal and are isosceles triangles, with hipotenuse a side of the square

Therefore we apply  Pythagoras theorem

Let   x be side of square, and r radius of the circle, ( diagonals touch the circle) then

x²  =  r² + r²

x²  = 2r²

x   =  √2 * r

Now Aea of square is :

A  =  L²          where L is square side

A(r)  = √2 * r

Domain of A(r)    =   R { r, r > 0}