Question

The endpoints of a side of a square lie on a circle and the opposite side of the square is tangent to the circle at its midpoint. Find the ratio of the side of the square to the radius.

Answer 1

The ratio of the side of the square to the radius is equal to $\frac{2}{5} \cdot \sqrt{5}$.

How to find the ratio of two lines

In this question we must construct first a geometric diagram with all geometric figures explained in statement. By Pythagorean theorem we have the following relationship between the side length of the square ($l$) and the circle radius ($r$):

$r^{2} = l^{2}+0.25\cdot l^{2}$ (1)

$r^{2}=1.25\cdot l^{2}$

$\frac{l}{r} = \sqrt{\frac{4}{5} }$

$\frac{l}{r} = \frac{2}{5}\cdot \sqrt{5}$

The ratio of the side of the square to the radius is equal to $\frac{2}{5} \cdot \sqrt{5}$. $\blacksquare$

To learn more on ratios, we kindly invite to check this verified question: https://brainly.com/question/1504221