[Math] Calculating radius of circle through chords

circlesgeometry

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

enter image description here

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 $R=5\sqrt{13}$.

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