Circles in the plane

A circle in the plane is a perfectly round shape where every point on its edge, called the circumference, is the same distance from a central point known as the center. This distance is called the radius. Circles are fundamental in geometry and can be found in various real-world applications, from wheels to roundabouts. The area inside a circle can be calculated using the formula \( A = \pi r^2 \), where \( A \) is the area and \( r \) is the radius. The length around the circle, or circumference, is given by \( C = 2\pi r \).