Probability of a point lying inside a square which is inscribed in a circle

Question

CD and EF are two diameters of the circle shown in image and CEDF is a square inscribed in the circle. If a point inside the circle is randomly chosen what is the probability that the point will lie inside the square?

Answer 1

Here are some hints.

A common length of the square and the circle is the radius of the circle. If the radius of the circle is $1$, what is the area of the square?

The probability will be the ratio of the two areas.

Spoiler:

If the radius of the circle is $1$, then its area is $\pi$. If half of the diagonal of the square is $1$, then its side is $\sqrt{2}$ (think isoceles right triangle), making its area is $2$, and the probability is the ratio of the two areas, $2/\pi$.