The problem is about an equilateral triangle $ABC$ inscribed in a circle with a radius of 8 cm. We are tasked with finding the length of the side of the triangle.

Key Concepts:

1. Inscribed Equilateral Triangle: For an equilateral triangle inscribed in a circle, the relationship between the side of the triangle $s$ and the radius $R$ of the circle is given by the formula: $s = R \times \sqrt{3}$
2. Given Data: The radius of the circle $R = 8 \, \text{cm}$.

Solution:

Using the formula for the side length of an equilateral triangle inscribed in a circle: $s = R \times \sqrt{3}$ Substitute $R = 8 \, \text{cm}$: $s = 8 \times \sqrt{3} \, \text{cm}$ Thus, the side length of the triangle is $8\sqrt{3} \, \text{cm}$.

Correct Answer:

The correct option is B. 8√3 cm.

Would you like more details or have any questions? Here are 5 related questions to explore this further:

1. How would the formula for the side of the triangle change if it was not equilateral but another type of triangle?
2. Can you derive the formula $s = R \times \sqrt{3}$ for an equilateral triangle inscribed in a circle?
3. What would be the area of the equilateral triangle given the side length $s$?
4. How does the central angle of the circle relate to the angles of the inscribed equilateral triangle?
5. If the circle had a radius of 10 cm, what would the side length of the inscribed equilateral triangle be?

Tip: Always remember that an equilateral triangle inscribed in a circle has its center coinciding with the center of the circle, making it symmetric and ideal for using geometric relations with the radius.