I have a rectangle with dimensions of 5x2.5 cm, how big of a circle do I need in order to fit that rectangle in the top part of the circle

Question

I have a rectangle with width of 5 cm and height of 2.5cm and I am wondering how big of a circle do I need in order to fit that rectangle in the top part of the circle like I've shown in the image below?

Answer 1

We know the radius is the hypotenuse of a triangle with sides $5/2=2.5$ and $2.5$. Thus, you need a circle with radius

$$r=\sqrt{(2.5)^2+(2.5)^2}=\sqrt{25/2}=\frac{5}{\sqrt{2}}=3.54\ cm$$