Geometry - Parts of a Circle

The Circle and its Center: A circle is a closed curved shape where every point on the boundary is at the exact same distance from a fixed point inside called the center. Visually, if you place the sharp tip of a compass on paper and draw a line around it, the spot where the tip rested is the center.

Radius: The line segment connecting the center of the circle to any point on its boundary is called the radius, denoted by $r$. Visually, radii look like the spokes of a bicycle wheel, all starting from the center and touching the outer rim.

Diameter: A line segment that passes through the center and connects two points on the circle's boundary is called the diameter, denoted by $d$. Visually, the diameter is the longest possible line you can draw inside a circle, and it splits the circle into two equal halves.

Chord: Any straight line segment that joins two points on the circle's boundary is called a chord. The diameter is a special type of chord that passes through the center. Visually, a chord looks like a 'slice' line through the circle, but it doesn't necessarily have to go through the middle.

Circumference: The total length of the boundary or the perimeter of the circle is known as the circumference. Visually, if you were to wrap a piece of string perfectly around a circular bottle cap and then straighten the string out, the length of that string would be the circumference.

Arc: An arc is any part or portion of the circumference of a circle. Visually, an arc looks like a curved 'piece' of the circle's edge, similar to the shape of a rainbow or a bow.

Semicircle: Half of a circle is called a semicircle. It is formed by a diameter and the arc connecting its two endpoints. Visually, a semicircle looks like the letter 'D' or a protractor.