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

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:

Hence,

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

Therefore,

Step-by-step explanation:

Look at the picture.

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

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

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

Therefore

Given:

therefore

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)