The Square shown has a side of length 2 units. What is the radius of the circle? (Please explain) Please explain the process a bit, as I am completely lost and I do not know how to solve this at all.


You might use the following theorems and formulas:


*

*Centri-Peripheral-Theorem, see https://en.wikipedia.org/wiki/Inscribed_angle#Theorem

*$t = \tan(\alpha)$ then $\sin(2 \alpha) = \frac{2 t}{1+t^2}$

*$1 = r \sin(2 \alpha)$, $r$ is the radius of the cycle


From the picture you see $t = 1/2$ put it into the formuar and solve for $r$!
$$ 1 = r \sin(2 \alpha) = r \frac{2 \, (\frac{1}{2})}{1+(\frac{1}{2})^2} = \frac{4}{5} r $$
Therefore C is the right answer.
cklick here to view a sketch
