The chord of a circle of radius 17 cm is 30 cm long. Calculate the distance of the chord from the centre of the circle.

Analyze the question: A chord 30 cm long lies in a circle of radius 17 cm. We need the perpendicular distance from the centre to the chord.

Concept: The perpendicular from the centre of a circle to a chord bisects the chord. This gives a right-angled triangle with:

• Hypotenuse = radius = 17 cm
• One side = half the chord = 30 ÷ 2 = 15 cm
• Other side = the distance d we want

Solution (Pythagoras' theorem):

r² = d² + (half chord)²

17² = d² + 15²

289 = d² + 225

d² = 289 − 225 = 64

d = √64 = 8 cm

Answer: The distance is 8 cm, which is option C.

Tip: Look out for Pythagorean triples. Here 8, 15, 17 is a famous triple, so as soon as you see 15 and 17 in a circle-chord problem, the missing side is 8. Other common triples are 3-4-5, 5-12-13 and 7-24-25.