A chord, 7cm long, is drawn in a circle with radius 3.7cm. Calculate the distance of the chord from the centre of the circle

Analyze the question: We have a chord of length 7 cm in a circle of radius 3.7 cm. We need the perpendicular distance from the centre to the chord.

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

• Hypotenuse = radius = 3.7 cm
• One side = half the chord = 3.5 cm
• Other side = the distance d we want

Solution:

Using Pythagoras' theorem:

d² = r² − (half chord)²

d² = 3.7² − 3.5²

Use the difference of two squares:

d² = (3.7 − 3.5)(3.7 + 3.5) d² = (0.2)(7.2) d² = 1.44

d = √1.44 = 1.2 cm

Answer: The distance of the chord from the centre is 1.2 cm, which is option B.

Tip: When you see numbers like 3.7 and 3.5 in a circle-chord problem, use the difference of two squares, a² − b² = (a − b)(a + b). It is much faster than squaring each number, and it saves time in the exam hall.