Circle

A circle is a simple closed shape in geometry. It can be defined as a set of points in a plane that are equidistant from a fixed point called the center. Alternatively, it can be seen as the path traced by a point that moves while maintaining a constant distance from the center.

Parts of a Circle

• Center (Origin): The fixed point equidistant from all points on the circle.
• Radius (R): Distance from the center to any point on the circle. It is half of the diameter.
• Diameter (D): The largest distance between two points on the circle, passing through the center. D = 2 × R.
• Circumference (C): The distance around the circle. C = 2πR.
• Arc: A portion of the circumference.
• Major Arc: Arc longer than half the circumference.
• Minor Arc: Arc shorter than half the circumference.
• Chord: Line segment connecting two points on the circle. A chord through the center is the diameter.
• Secant: Line passing through the circle at two points, extended beyond the circle.
• Tangent: Line touching the circle at exactly one point.
• Sector: Area enclosed between two radii.
  • Major Sector: Central angle > 180°
  • Minor Sector: Central angle < 180°

The Constant Pi (π)

The radius, diameter, and circumference are related using π (pi), which is the ratio of the circumference to the diameter. Approximate value: π ≈ 3.14159.

Pi is an irrational number (cannot be expressed exactly as a fraction) and a transcendental number (not the root of any polynomial with rational coefficients).

Historically, geometers attempted to “square the circle” using only a compass and straightedge. In 1880, Ferdinand von Lindemann proved that π is transcendental, showing that squaring the circle is impossible.

Circle Formulas

Where:

• R = Radius
• D = Diameter
• C = Circumference
• A = Area
• π ≈ 3.14159