Circle Terminology

Intuition and core definition

A circle is the set of points in a plane at a fixed distance from a centre; the filled region is a disk. A radius joins centre to circle, a diameter is a centre-crossing chord, a chord joins two circle points, a secant intersects twice, and a tangent touches once locally.

Notation, language, and conditions

$r$ denotes radius, $d=2r$ diameter, $C=2\pi r$ circumference, and $A=\pi r^2$ disk area. A central angle has vertex at the centre; an inscribed angle has vertex on the circle. Arcs are named by endpoints, with a third point used to specify a major arc.

Why this idea matters

Precise circle vocabulary distinguishes centre-based segments, boundary portions, and lines that meet the circle in different numbers of points.

A dependable method

1. Locate the centre and determine whether points lie inside, on, or outside.
2. Classify segments by endpoints and whether they pass through the centre.
3. Classify lines by the number of intersections with the circle.
4. Name angles by vertex location and identify intercepted arcs.
5. Use the exact term before selecting any associated theorem.

Worked example

Common mistakes