Chord-Centre Theorem — O/L Mathematics

What must I remember about Chord-Centre Theorem?

• Theorem 1: The perpendicular drawn from the centre of a circle to a chord bisects the chord (if OM ⊥ AB, then AM = MB).
• Converse Theorem 1: The straight line joining the centre of a circle to the midpoint of a chord is perpendicular to the chord (if AM = MB, then OM ⊥ AB).
• Pythagorean relationship: In right-angled triangle OAM, r² = d² + (c / 2)², where r = radius (OA), d = perpendicular distance from centre (OM), and c = chord length (AB).
• Theorem 2: Chords of a circle that are equal in length are equidistant from the centre of the circle.
• Converse Theorem 2: Chords that are equidistant from the centre of a circle are equal in length.

Test yourself (1 minute)

1. Radius as hypotenuse

   In the right-angled triangle formed by the radius, half-chord, and perpendicular distance, the RADIUS (r) is always the hypotenuse opposite the right angle.

2. Diameter vs radius trap

   If diameter is given in the problem, divide by 2 to obtain radius r before applying Pythagoras' theorem.

3. Distance between parallel chords

   For two parallel chords on OPPOSITE sides of the centre, sum their distances (d₁ + d₂); for chords on the SAME side of the centre, subtract their distances (|d₁ - d₂|).

Practise Chord-Centre Theorem questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 26)

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Where does Chord-Centre Theorem fit in the syllabus?

Grade 10 · Term 3