It looks like a simple question, but for some reason I just can't figure out how to do it: I am given the following circle (see picture) and need to calculate the radius. I know how this works when you know the chord height, but not when you are given line segments as shown.
Thanks in advance.
Best Answer
Use the Law of sines
Let $R$ the circumradius of the triangle $ABC$ \begin{align*} \frac{|AC|}{\sin B}&=2R\\[4pt] \frac{\sqrt{2^2+4^2}}{\frac2{\sqrt{2^2+16^2}}}&=2R\\[4pt] \frac{\sqrt{20}\sqrt{260}}{2}&=2R \end{align*}
Then $R=5\sqrt{13}$.