Yet Another Geometry Problem

Geometry Level 2

The ratio of the areas of the incircle and the circumcircle of a square is?

3:4

1:\sqrt{2}

1:2

\sqrt{2}:\frac{1}{2}

2 solutions

Mardokay Mosazghi
Jun 29, 2014

$s$ =side of the square

The diameter of incircle = $s/2$ area of incircle = $\pi*(s/2)^2 = \pi*(s^2/4)$

Diamerter of circle = $2*s$ => area of circumcircle = $\pi*(2*s/2)^2 = \pi*(s^2/2)$

ratio = (area of incircle)/(area of circumcircle)= $\pi*(s^2/4) / \pi*(s^2/2) =1:2$

ans 1:2

Maybe using "\pi" instead of pi to obtain $\pi$ would make it look better. :)

Sudeep Salgia - 6 years, 11 months ago

thanks fixed

Mardokay Mosazghi - 6 years, 11 months ago

Bernardo Sulzbach
Jul 1, 2014

$\frac{A_c}{A_i}=\frac{R^2}{r^2}=\frac{\left(\frac{l\sqrt{2}}{2}\right)^2}{\left(\frac{l}{2}\right)^2}=2$