Answer:
20 cm
Step-by-step explanation:
Let a cm be the length of the side of equilateral triangle.
Use formula for the radius of inscribed circle into the equailteral triangle:
[tex]r_{inscribed}=\dfrac{a\sqrt{3}}{6}[/tex]
Hence,
[tex]\dfrac{a\sqrt{3}}{6}=10\Rightarrow a=\dfrac{60}{\sqrt{3}}[/tex]
Now, use formula for the circumscribed circle's radius:
[tex]R_{circumscribed}=\dfrac{a\sqrt{3}}{3}[/tex]
Therefore,
[tex]R_{circumscribed}=\dfrac{\frac{60}{\sqrt{3}}\cdot \sqrt{3}}{3}=20\ cm[/tex]
