Question

In the following figure, the square ABCD is inscribed in the circle centered at point P. What is the area of the circle?

Answer 1

`A_(Circle) \approx 39.24\: units^2`

Explanation:

Square ABCD is inscribed in a circle with center P such that BC = 5 units.

BD will be diagonal of the square as well as diameter of the circle.

`BD = BC*\sqrt 2`

`\implies BD = 5\sqrt 2`

-> Diameter of the circle
`(d) = 5\sqrt 2`

-> Radius of the circle
`(r) = 2.5\sqrt 2=3.535\: units`

`A_(Circle) =\pi(r)^2`

`\implies A_(Circle) =3.14(3.535)^2`

`\implies A_(Circle) =3.14(3.535)^2`

`\implies A_(Circle) =39.2381465`

`\implies A_(Circle) \approx 39.24\: units^2`