Two circles of equal radius 7 cm overlap such that the centre of each circle lies on the circumference of the other. Find the perimeter of the OVERLAPPING (lens-shaped) region. (Take π = 22/7.)
Show Worked Solution
Worked Solution
Step 1: When centres lie on each other's circumference, the overlap subtends 120° at each centre (forming an equilateral triangle).
Step 2: Each arc length = (120°/360°) × 2π × 7 = (1/3) × 44 = 44/3 ≈ 14.67 cm.
Step 3: Lens perimeter = 2 arcs = 2 × 14.67 ≈ 29.33 cm.
Answer: 29.33 cm
Correct answer: 29.33 cm
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