Circles • Topic 1 of 3

Radius, Diameter, Chord, Arc, and Sector

What is a circle and its basic parts? A circle is a perfectly round, flat shape where every single point on its boundary is exactly the same distance from a fixed central point called the center. Think of a bicycle wheel, a round dinner plate, or a shiny coin.

To map and measure a circle, we use several essential geometric components:

  • A radius is a straight line segment drawn from the center of the circle to any point on its outer edge. (Plural: radii). Think of it like a single spoke on a bicycle wheel.
  • A diameter is a straight line segment that passes directly through the center, connecting two opposite points on the boundary. It is the widest distance across the circle and is exactly double the length of the radius (\(d = 2r\)). Think of it like a line cutting a pizza perfectly in half.
  • A chord is any straight line segment that links two points on the circle's edge. The diameter is a special chord—in fact, it is the longest possible chord in any circle!
  • An arc is a curved portion or section of the circle's outer boundary line. Think of the crust on a single slice of pie. A small piece is a minor arc, while the large remaining loop is a major arc.
  • A sector is a pie-slice region enclosed between two radii and the arc connecting them. Think of a slice of watermelon or a Trivial Pursuit game piece. A small slice is a minor sector, and the rest of the circle is the major sector.
Geometric FeatureDefinitionRelationship / Key Characteristic
Radius (\(r\))Center point to edge boundaryHalf the length of the diameter
Diameter (\(d\))Edge to edge, passing through centerLongest possible chord (\(d = 2r\))
ChordEdge to edge straight lineDoes not have to pass through center
ArcPart of the curved boundary pathCategorized into minor and major arcs
SectorRegion enclosed by two radii and an arcResembles a standard slice of pie
PARTS OF A CIRCLE O (centre) radius r diameter = 2r chord arc sector KEY FORMULAS d = 2r r = d / 2 C = 2πr A = πr² π ≈ 3.14 or 22/7 Circumference = perimeter
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Worked Example
A circular wall clock has a radius of \(14\text{ cm}\). Find the length of its diameter.
Solution*Step 1: Identify the given value, which is the radius (\(r = 14\text{ cm}\)). *Step 2: Use the mathematical formula connecting radius and diameter:* \(d = 2r\) *Step 3: Substitute the value into the formula:* \(d = 2 \times 14\text{ cm}\) *Step 4: Calculate the final value:* \(d = 28\text{ cm}\)

Key Points

  • A circle's radius goes from the center to the edge; the diameter cuts all the way across through the center.
  • The diameter is always exactly twice as long as the radius (\(d = 2r\)).
  • A chord is any line between two points on the edge, making the diameter the longest chord.
  • An arc is a piece of the perimeter loop; a sector is a slice of the interior space bounded by two radii.
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Tap an option to check your answer0 / 4
Q1.The diameter is ___ the radius.
Explanation: $d=2r$.
Q2.The longest chord of a circle is the:
Explanation: Diameter.
Q3.A chord joins:
Explanation: Two points on the circle.
Q4.A sector is bounded by two radii and an:
Explanation: Arc.