Find the radius of the circle circumscribed around an equilateral triangle, if the radius of the circle inscribed into this triangle is 10 cm.

Answer:20 cmStep-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]