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 Ο: $C = 2\pi r$, or equivalently $C = \pi d$.
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. (The length of an arc is its own topic, covered in arc length.)
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. The area of a sector is a fraction of the whole circle's area, set by its central angle, and the full method lives in sector of a circle.
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. A segment and a sector are easy to confuse, so hold the difference: a sector is bounded by two radii and an arc, while a segment is bounded by one chord and an arc.
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. More on chords sits in chord of a circle.
Tangent: A tangent is a straight line that touches the circle at exactly one point, never crossing into it. A key fact: a tangent is always perpendicular to the radius drawn to the point where it touches. That right angle is the single most-used property of tangents in problems.
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, so a secant is a chord extended in both directions.
The fastest way to keep the three lines straight: a tangent touches once, a secant cuts twice, and a chord is the inside part of a secant.
Examples of the Parts of a Circle
With every part named, here is each one doing actual work, from a one-step identification up to a problem that uses several parts together. The problems build from reading a diagram to calculating with the formulas the parts carry.
Example 1: A circle has a radius of 7 cm. Find its diameter and circumference. Use $\pi = \dfrac{22}{7}$
The diameter is twice the radius, and the circumference is $2\pi r$:
$$d = 2r = 14 \text{ cm}, \qquad C = 2\pi r = 2 \times \tfrac{22}{7} \times 7 = 44 \text{ cm}.$$
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
A first instinct is to add the radius and the 8 cm along the line, giving $6 + 8 = 14$ cm. Check that against the picture. The radius runs to the point of contact, and the line P sits on is the tangent, so the radius and the tangent meet at a right angle, not in a straight line. Adding them would only be correct if they pointed the same way, but they are perpendicular, so they form the two legs of a right triangle, not a straight path.
The correct move uses the tangent-perpendicular-radius property and the Pythagorean theorem, with the distance to the centre as the hypotenuse:
$$OP^2 = r^2 + 8^2 = 6^2 + 8^2 = 36 + 64 = 100, \qquad OP = \sqrt{100} = 10 \text{ cm}.$$
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
(a) Diameter. (b) Sector. (c) Secant.
Final answer: (a) diameter, (b) sector, (c) secant.
Example 4: A sector of a circle of radius 10 cm has a central angle of $90Β°$. Find its area. Use $\pi = 3.14$
A sector's area is the fraction $\dfrac{\theta}{360Β°}$ of the whole circle's area:
$$\text{Area} = \frac{\theta}{360Β°} \times \pi r^2 = \frac{90}{360} \times 3.14 \times 10^2 = \frac{1}{4} \times 314 = 78.5 \text{ cm}^2.$$
Final answer: 78.5 cmΒ².
Example 5: A chord 24 cm long lies 5 cm from the centre of a circle. Find the radius
The perpendicular from the centre bisects the chord, so the half-chord is 12 cm. The radius, half-chord, and perpendicular form a right triangle:
$$r^2 = 12^2 + 5^2 = 144 + 25 = 169, \qquad r = \sqrt{169} = 13 \text{ cm}.$$
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
Both regions share the same arc, but they are bounded differently. The minor segment is enclosed by the chord and the minor arc above it. The minor sector is enclosed by the two radii to the chord's endpoints and the same minor arc. The sector includes the triangle between the two radii and the chord; the segment is the sector with that triangle removed.
Final answer: a segment is bounded by a chord and an arc; a sector is bounded by two radii and an arc, so segment = sector minus the central triangle.
Where the Parts of a Circle Show Up
Naming the parts is not just exam vocabulary; each part is a tool a designer reaches for in a specific situation.
Wheels and clocks. The radius sets how far a wheel rolls per turn (one rotation covers the circumference); a clock face is read in sectors, each hour a $30Β°$ slice.
Roads and rail. Engineers lay out curved roads using arcs, and the straight sight-line across a bend is a chord. The tangent direction at a point on a curve is the direction a car is actually pointing.
Architecture and design. Arched windows and domes are built from segments and arcs; a circular stadium's seating is divided into sectors.
Optics and signals. A tangent line models a light ray grazing a curved lens, and the perpendicular-to-the-radius rule is what predicts where it reflects.
For a student meeting circles for the first time, getting the parts straight is the foothold for everything that follows, area, circumference, the circle theorems, even the equation of a circle in coordinate geometry. Each later topic is just one of these parts studied more deeply.
Where Students Trip Up on the Parts of a Circle
Mistake 1: Confusing a chord with the diameter
Where it slips in: A student calls any line across the circle a diameter, even when it misses the centre.
Don't do this: Treat every chord as a diameter.
The correct way: Only a chord through the centre is a diameter. A chord that misses the centre is shorter, and the diameter is the longest chord of all. The second-guesser who knows the difference but doubts it should check one thing: does the line pass through the centre?
Mistake 2: Mixing up a sector and a segment
Where it slips in: A student labels the pie-slice region a segment, or the chord-cut region a sector.
Don't do this: Use the two words interchangeably.
The correct way: A sector is bounded by two radii and an arc (a pizza slice); a segment is bounded by a chord and an arc (the orange-slice piece). Two straight edges from the centre means sector; one straight chord means segment.
Mistake 3: Forgetting the tangent meets the radius at a right angle
Where it slips in: A student treats the radius and tangent as lying along the same line.
Don't do this: Add the radius to a tangent length as if they were collinear.
The correct way: A tangent is always perpendicular to the radius at the point of contact, so the two are the legs of a right triangle. Mark the right angle before using any tangent length, as in Example 2.
Key Takeaways
The main parts of a circle are the centre, radius, diameter, circumference, chord, arc, sector, segment, tangent, and secant.
The centre and radius define the circle; the diameter is $2r$ and the circumference is $2\pi r$.
A sector is bounded by two radii and an arc; a segment is bounded by a chord and an arc, which is the difference students miss most.
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, and concentric circles share a centre but differ in radius.
Practice These Problems to Solidify Your Understanding
A circle has a diameter of 20 cm. State its radius and circumference (use $\pi = 3.14$).
A tangent from an external point P touches a circle of radius 9 cm; P is 12 cm from the point of contact. Find the distance from P to the centre.
Name the part of a circle bounded by a chord and the arc above it.
Answer to Question 1: radius 10 cm, circumference 62.8 cm. Answer to Question 2: 15 cm. Answer to Question 3: a segment. If Question 2 gave you 21, you added the radius and tangent instead of using the right angle (see Mistake 3).
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