Parts of a Circle: Names, Definitions & Diagram

TL;DR

The main parts of a circle are the centre, radius, diameter, circumference, chord, arc, sector, segment, tangent, and secant, every one of them defined by its relationship to the single fixed centre point. This article names and explains each part with a labelled diagram, the formulas tied to them, six worked examples, and the common mistakes students make.

What Are the Parts of a Circle?

A circle is the set of all points that sit the same distance from one fixed point. That fixed point is the centre, and the equal distance is the radius. Every part below is named by how it relates to those two things. There are ten parts worth knowing, and they fall into three natural groups: the centre and the distances (centre, radius, diameter, circumference), the regions and curves inside or along the circle (arc, sector, segment), and the lines that meet the boundary (chord, tangent, secant).

The Centre and the Distances

Centre. The centre is the single fixed point that the whole circle is built around. It is usually labelled O. Every point on the circle is exactly the same distance from it.

Radius. The radius is the distance from the centre to any point on the boundary, written as r. A circle has infinitely many radii, all equal in length. The radius is the building block for almost every circle formula.

Diameter. The diameter is the distance straight across the circle through the centre, written as d. It is made of two radii in a line, so it is always twice the radius: d=2r.

Circumference. The circumference is the distance all the way around the circle, its perimeter. It relates to the radius through π: C=2πr, or equivalently C=πd.

The Curves and Regions

Arc: An arc is a curved piece of the circumference, a portion of the boundary between two points. The shorter of the two pieces is the minor arc; the longer is the major arc.

Sector: A sector is the pie-slice region enclosed by two radii and the arc between them, like a slice of pizza. A larger slice is the major sector; a smaller one is the minor sector.

Segment: A segment is the region cut off by a chord and the arc above it, like the piece of an orange left after a straight slice. The smaller piece is the minor segment; the larger is the major segment.

The Lines That Meet the Boundary

Chord: A chord is a straight segment joining any two points on the boundary. The diameter is the longest chord of all, because it passes through the centre.

Tangent: A tangent is a straight line that touches the circle at exactly one point, never crossing into it. A tangent is always perpendicular to the radius drawn to the point where it touches.

Secant: A secant is a straight line that cuts the circle at two points. A chord is just the piece of a secant that lies inside the circle.

Examples of the Parts of a Circle

Example 1: A circle has a radius of 7 cm. Find its diameter and circumference. Use π=227.

The diameter is twice the radius, and the circumference is 2πr:

d=2r=14 cm, C=2πr=44 cm.

Final answer: diameter 14 cm, circumference 44 cm.

Example 2: A line touches a circle of radius 6 cm at a single point, and a point P on that line is 8 cm from the point of contact. Find the distance from P to the centre.

The correct move uses the tangent-perpendicular-radius property and the Pythagorean theorem:

OP²=r²+8²=10 cm.

Final answer: OP = 10 cm.

Example 3: In a circle, name the part described in each case: (a) the distance straight across through the centre, (b) the region between two radii and an arc, (c) a line cutting the circle at two points.

Final answer: (a) diameter, (b) sector, (c) secant.

Example 4: A sector of a circle of radius 10 cm has a central angle of 90°. Find its area. Use π=3.14.

Area=θ360°×πr²=78.5 cm².

Final answer: 78.5 cm².

Example 5: A chord 24 cm long lies 5 cm from the centre of a circle. Find the radius.

Final answer: r = 13 cm.

Example 6: Explain the difference between the minor segment and the minor sector cut off by the same chord and arc.

Final answer: a segment is bounded by a chord and an arc; a sector is bounded by two radii and an arc.

Where the Parts of a Circle Show Up

Wheels and clocks. The radius sets how far a wheel rolls per turn; a clock face is read in sectors.
Roads and rail. Engineers lay out curved roads using arcs, and the straight sight-line across a bend is a chord.
Architecture and design. Arched windows and domes are built from segments and arcs.
Optics and signals. A tangent line models a light ray grazing a curved lens.

Where Students Trip Up on the Parts of a Circle

Mistake 1: Confusing a chord with the diameter.

Mistake 2: Mixing up a sector and a segment.

Mistake 3: Forgetting the tangent meets the radius at a right angle.

Key Takeaways

The main parts of a circle are the centre, radius, diameter, circumference, chord, arc, sector, segment, tangent, and secant.
A sector is bounded by two radii and an arc; a segment is bounded by a chord and an arc.
A tangent touches once and is perpendicular to the radius; a secant cuts twice; a chord is the inside part of a secant.
The diameter is the longest chord.