Question

11(b) A chord, 20cm long, is 12cm from the centre of the circle. Calculate, correct to one decimal place, the: (i) Angle subtended by the chord at the centre of the circle; (ii) Perimeter of the minor segment cut off by the chord. [Take π=3.142]

Accepted Answer

Radius r=√(12²+10²)=√(144+100)=√244... using half-chord=10cm and perpendicular distance=12cm: tan(θ/2)=10/12=0.833, θ/2=tan^-1(0.833)=39.8°, θ=79.6° (1 d.p.) — the angle subtended at the centre. (ii) r=√(12²+10²)=√244≈15.62cm. Length of arc = (θ/360)x2πr = (79.6/360)x2x3.142x15.62 ≈ 21.703cm. Perimeter of minor segment = chord + arc = 20+21.703 = 41.7cm (1 d.p.).

WAEC Mathematics 2017 Theory — Question 21

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