A chord subtends an angle of 120o at the centre of a circle of radius 3.5cm. Find the perimeter of the minor…

Analyze the question: A chord subtends 120° at the centre of a circle of radius 3.5 cm. We need the perimeter of the minor sector. A sector's perimeter is the arc length plus the two radii.

Concept:

• Arc length = (θ/360) × 2πr
• Perimeter of sector = arc length + 2r

Solution:

Arc length = (120/360) × 2 × (22/7) × 3.5 = (1/3) × 22 = 22/3 = 7⅓ cm

Two radii = 2 × 3.5 = 7 cm

Perimeter = 7⅓ + 7 = 14⅓ cm

Check against options: 14⅓ cm matches option A.

Option D (7⅓ cm) is only the arc length. It is a trap for students who forget to add the two radii.

Tip: For the perimeter of a sector, always add the two radii to the arc length. Perimeter of sector = (θ/360 × 2πr) + 2r. If you were asked for the perimeter of the segment instead, you would add the chord length to the arc.