Mathematics for IGCSE & O level - Mensuration (Section 3 - No. 1)
The perimeter of the minor segment of a circle of radius 5 cm with a 120° angle is...
10 + 5π/3
5 + 10π/3
10 + 10π/3
5 + 5π/3
Explanation
Perimeter is the arc length + the chord length. The arc length = (120/360) * 2 * π * 5 = 10π/3 cm. The chord length = 2 * r * sin(θ/2) = 2 * 5 * sin(120/2) = 10 * sin(60) which can be worked out as 10.
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