In a circle radius rcm, a chord 16$\sqrt{3}cm$ long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r

Analyze the question: A chord is 16√3 cm long and lies 10 cm from the centre. The perpendicular from the centre to a chord bisects the chord, so we can form a right-angled triangle.

Concept: The radius r is the hypotenuse. The two other sides are:

• the distance from the centre to the chord = 10 cm
• half the chord = (16√3)/2 = 8√3 cm

Solution (Pythagoras):

r² = 10² + (8√3)² r² = 100 + 64 × 3 r² = 100 + 192 r² = 292

r = √292 ≈ 17.09 cm

To the nearest cm, r ≈ 17 cm.

Check against the options: 17 cm is option B.

Tip: Whenever a question gives a chord and its distance from the centre, draw the perpendicular from the centre. It bisects the chord, which gives you a right-angled triangle to apply Pythagoras. Also remember (a√b)² = a²b, so (8√3)² = 64 × 3 = 192. Quick checks like 17² = 289, which is close to 292, help confirm your answer.