Find the area of a circle and the length of its circumference if the side of a regular triangle inscribed in it is 4 cm.

1. Draw the radii in the inscribed triangle. Then each central angle will be equal to 120 degrees (since the degree measure of the central angle is 2 times larger than the inscribed one, and the last one (by the property of a regular triangle) is 60).
2. Construct the perpendicular CH and consider the VON triangle. The HBO angle is 30 degrees, its cosine is (√3) / 2. In this case, the cosine can be represented as HB / VO, where HB = 2 (half of the side of the original triangle), VO is the radius.
3. Express the radius: BO = 4 / (√ 3)
4. Circumference: 8pi / (√ 3)
5. Area of a circle: 16pi / 3