As you know an equilateral triangle have three sides of all equal lengths, that being

2√3. The radius of your circle will then touch each side of your triangle exactly in the middle of each side so you have one side of a triangle being √3, one side being the unknown radius, and the last side being the center of the circle and center of the equilateral triangle to each of the vertices. (It helps to draw this on paper.) So now you want to apply the formula of an equilateral h(height) = √3 ÷ 2 × s(sides) where s is equal to each side of your equilateral triangle. Your answer should equal one.

2√3. The radius of your circle will then touch each side of your triangle exactly in the middle of each side so you have one side of a triangle being √3, one side being the unknown radius, and the last side being the center of the circle and center of the equilateral triangle to each of the vertices. (It helps to draw this on paper.) So now you want to apply the formula of an equilateral h(height) = √3 ÷ 2 × s(sides) where s is equal to each side of your equilateral triangle. Your answer should equal one.