Question

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 1

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:

$r_{inscribed}=\dfrac{a\sqrt{3}}{6}$

Hence,

$\dfrac{a\sqrt{3}}{6}=10\Rightarrow a=\dfrac{60}{\sqrt{3}}$

Now, use formula for the circumscribed circle's radius:

$R_{circumscribed}=\dfrac{a\sqrt{3}}{3}$

Therefore,

$R_{circumscribed}=\dfrac{\frac{60}{\sqrt{3}}\cdot \sqrt{3}}{3}=20\ cm$

Answer 2

Answer:

20 cm

Step-by-step explanation:

Look at the picture.

The formula of a radius of a circle circumscribed around an equaliteral triangle:

$R=\dfrac{2}{3}\cdot\dfrac{a\sqrt3}{2}$

The formula od a radius of a circle inscribed into an equaliteral triangle:

$r=\dfrac{1}{3}\cdot\dfrac{a\sqrt3}{2}$

As you can see in the formulas above, the radius of the circumscribed circle is twice the radius of the inscribed circle.

Therefore

$R=2r$

Given:

$r=10\ cm$

therefore

$R=2(10\ cm)=20\ cm$