Welcome! Today we'll explore one of the most fundamental shapes in geometry: the circle. A circle is a round shape that consists of all points in a plane that are at exactly the same distance from a central point. This central point is called the center, and the fixed distance is called the radius.
Now let's identify the key parts of a circle. The center is the fixed point at the middle of the circle. The radius is the distance from the center to any point on the edge. The diameter is the distance straight across the circle through the center, which is twice the radius. Finally, the circumference is the distance around the entire circle.
Circles have important mathematical formulas. The area of a circle is pi times the radius squared. The circumference is two pi times the radius. And the diameter is simply twice the radius. Let's see how these values change as we adjust the radius of our circle.
Let's see how to draw a circle step by step. First, we mark the center point. Then we choose our radius length. The key is to keep this distance constant as we move around the center. By drawing all points that are exactly this distance from the center, we create a perfect circle. Watch as we trace the circle by rotating around the center point.