Circle, sector, segment, etc.

A circle is the set of all points in a plane at a fixed distance (radius $r$) from a fixed point (center $O$). Important parts include:

• Radius: $OA$ for point $A$ on the circle
• Diameter: a chord passing through $O$, length $2r$
• Chord: any segment joining two points on the circle
• Arc: a continuous part of the circumference between two points
• Sector: the region bounded by two radii and the arc between them
• Segment: the region bounded by a chord and the arc between its endpoints

Important properties

• All radii of a circle are equal.

• The diameter is the longest chord.

• A sector's area is proportional to its central angle.

• A segment is smaller than the corresponding sector (unless the chord is a diameter).