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Chapter 5 · Period 1 of 15 · 50 min

Defining the Circle: Centre, Radius, Chord, Diameter

Definitions · Deductive

This unit establishes the foundational vocabulary the entire chapter builds on: locus, centre, radius, chord, and diameter. Watch for the common conflation of radius with diameter — students may halve or double values incorrectly in later calculations. Example 4, p.19 is not present in this chapter, but teachers may direct students to re-read the opening page of Section 5.1 independently for additional grounding.

0-10Open by presenting the locus definition of a circle: every point on the circle is at the same fixed distance (the radius) from a fixed point (the centre). Ask students to state what changes and what stays fixed when different circles are drawn from the same centre, establishing that radius determines size.
10-25Formally define radius, chord, and diameter using the board diagram. Derive that the diameter equals twice the radius and that the diameter is the longest chord. Students write their own definitions in mathematical language, then compare with a partner.
25-40Present the think-and-reflect prompt from Section 5.1: how might Amina locate the centre of a circular piece of paper? Students reason individually, then share: folding the paper twice along two different diameters gives the centre as their intersection, linking back to the locus definition.
40-50Students use compass and ruler to draw a circle, mark its centre, draw two different chords, and verify with a ruler that the diameter they draw is the longest chord. They write one sentence justifying this using the locus definition.
Assessment

Competency (C-4.3). Prove and apply properties of circles including chord, subtended-angle, and inscribed-polygon relationships.

Learning outcome. Students can state the locus definition of a circle and identify radius, chord, and diameter in a given circle diagram.

A circle has centre O and radius 5 cm. Points P and Q lie on the circle such that PQ passes through O. Which of the following correctly describes PQ?

  • A PQ is a chord of length 5 cm.
  • B PQ is a chord of length 5 cm that does not pass through the centre.
  • C PQ is a diameter of length 10 cm.
  • D PQ is a radius of length 5 cm.

C. PQ is a diameter of length 10 cm.

What each wrong option reveals

  • A Confuses diameter with radius: takes the length of PQ as the radius (5 cm) rather than twice the radius, misreading 'passes through O' as defining a chord equal to r.
  • B Correctly identifies PQ as a chord but contradicts the given condition that PQ passes through O, showing a disconnect between the definition of diameter and the chord category.
  • D Conflates radius and diameter: labels PQ as a radius even though it joins two points on the circle, not one point to the centre.
Chapter 5 · 15 periods of 50 min

Also saved as 9 periods or 12 periods.

  • 2Rotational and Reflection Symmetries of a Circle
    Symmetries of a Circle
  • 3How Many Circles Pass Through Two or Three Points?
    How Many Circles?
  • 4Equal Chords and the Central Angles They Subtend
    Chords and the Angles They Subtend
  • 5Perpendicular from Centre to a Chord Bisects It
    Midpoints and Perpendicular Bisectors of Chords
  • 6Equal Chords Are Equidistant from the Centre
    Distance of Chords from the Centre
  • 7Longer Chord Lies Closer to the Centre
    Which of the two unequal chords is farther from the centre?
  • 8Arcs: Major, Minor, and the Angle at the Centre
    Angles Subtended by an Arc
  • 9Central Angle Is Double the Inscribed Angle
    Angle subtended by an arc at a point on the circle outside the arc
  • 10Equal Inscribed Angles and the Concyclicity of Four Points
    Concyclicity of Points
  • 11Constructing Circumcircles and Applying Theorem 1
    How Many Circles? (Revisit)
  • 12Applying the Chord-Distance Formula to Problem Sets
    Distance of Chords from the Centre (Revisit)
  • 13Applying Theorems 9, 10, and 11 to Cyclic Angle Problems
    Concyclicity of Points (Revisit)
  • 14Proof Practice: Concyclicity, Chord Bisectors, and Cyclic Properties
    Concyclicity of Points (Revisit)
  • 15Whole-Chapter Synthesis: Connecting Circle Theorems
    Synthesis
Ganita Manjari · Class 9 · 14 chapters

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