Geometry - Introduction to Circles

A circle is a simple closed curved shape where every point on the boundary is at an equal distance from a fixed point inside called the center. If you trace the edge of a round coin or a bottle cap on a piece of paper, you create a circle.

The Center is the fixed point in the exact middle of the circle, often labeled with a letter like $O$. All points on the circle's boundary are at the same distance from this central point.

The Radius (plural: radii) is a straight line segment that connects the center of the circle to any point on its boundary. Visually, it looks like a single spoke of a bicycle wheel. Every circle has many radii, and they are all equal in length.

The Diameter is a straight line segment that passes through the center of the circle and has its endpoints on the circle's boundary. It is the longest line that can be drawn inside a circle and divides the circle into two equal halves. The diameter is always twice the length of the radius.

A Chord is a line segment that joins any two points on the circle's boundary. Unlike the diameter, a chord does not have to pass through the center. However, the diameter is special because it is the longest chord in any circle.

The Circumference is the total length of the circle's boundary. You can think of it as the 'perimeter' of the circle. If you were to wrap a string around a circular object and then lay that string flat, the length of that string is the circumference.

A Semicircle is exactly half of a circle. A diameter divides a circle into two semicircles. Visually, it looks like a 'D' shape or a half-moon.

The Interior and Exterior of a circle refer to the space inside and outside the boundary. Points inside the circle's boundary are in the interior, while points outside are in the exterior. Points on the boundary line itself are said to be 'on the circle'.