Two squares are inscribed in a semi-circle, as shown below. Find the radius of the semi-circle.

Find the radius of the semicircle.

Let the side length of the squares be s.

Case A) Squares next to each other.

Then the radius of the semicircle is $\color{blue}r=s\sqrt{2}.$

Case B) Squares on top of each other.

Then the radius of the semicircle is:

$r^2=(2s)^2+(\frac{s}{2})^2\\ r=\sqrt{\frac{4\cdot4s^2+s^2}{4}}\\ \color{blue}r=\frac{s}{2}\sqrt{5}$

 !