Carts and Wheels - Radius and Diameter

A circle is a perfectly round flat shape with no corners or sides. Visually, it is like a ring where every point on the boundary is the same distance from a fixed point in the middle called the center.

The center is the exact middle point of the circle. If you place a compass point at the center to draw a circle, the distance to the pencil tip remains constant as you rotate it.

The radius ($r$) is the distance from the center of the circle to any point on its edge. Visually, it looks like a single spoke of a bicycle wheel connecting the center hub to the outer rim.

The diameter ($d$) is a straight line passing through the center, connecting two points on the circle's edge. It is the longest line that can be drawn inside a circle and acts like a line of symmetry that cuts the circle into two equal halves.

The diameter is always exactly twice the length of the radius. If you place two radii end-to-end in a straight line passing through the center, they form the diameter.

Every circle has many possible radii and diameters, but in any specific circle, all radii are equal in length and all diameters are equal in length.

When drawing a circle with a compass, the distance between the metal point and the pencil lead represents the radius of the circle.