Chord-Centre Theorem — O/L Mathematics

How do I practise Chord-Centre Theorem?

1 question with a worked solution

1. A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the perpendicular distance from the centre of the circle to the chord.
   1. A) 6 cm
   2. B) 5 cm
   3. C) 8 cm
   4. D) 7 cm
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   Correct answer: A) 6 cm

   The perpendicular from the centre to a chord bisects the chord (half chord = 16/2 = 8 cm). By Pythagoras' theorem in the right triangle: d² + 8² = 10² → d² + 64 = 100 → d² = 36 → d = 6 cm.

   Show worked solution

   Step 1: Apply theorem: perpendicular from centre bisects chord → half chord = 16 / 2 = 8 cm. Step 2: Form right-angled triangle with radius as hypotenuse (10 cm) and half-chord as one leg (8 cm). Step 3: Pythagoras' theorem: d = √(10² - 8²) = √(100 - 64) = √36 = 6 cm. Answer: 6 cm.
   Modelled on: the O/L Mathematics examination pattern

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Where does Chord-Centre Theorem fit in the syllabus?

Grade 10 · Term 3