A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle?

Name: A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle?
Uploaded: Sept. 30, 2021, 12:14 p.m.
Duration: 2 min 6 s
Description: A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle?

Solution

As we know that area of the circle is directly proportional to the square of its radius.
Hence $$\frac{A_{ic}}{A_{cc}} = \frac{\frac{x^2}{4}}{\frac{x^2}{2}}$$
Where $$x$$ is side of square (say), ic is inscribed circle with radius $$\frac{x}{2}$$, cc is circumscribed circle with radius $$\frac{x}{\sqrt{2}}$$
So ratio will be 1:2