XY is a chord of a circle of radius 5cm, subtending an angle of 50° at the centre. Find
(a) the length of the chord XY.
(b) the length of the arc XY correct to 3 sign. Figures
(c) proof that XY is the chord of the circle?
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Asked by Melo on 1st August, 2020
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1 week ago
Length of a chord= 2rsin(θ/2)
θ= 50° and r= 5cm
y= 2(5)(sin 25°)= 10sin25°= 4.23cm
(II) z= ?
Length of an arc= (θ/360)2πr
z= (50/360)2(π)(5)= 4.36cm in 3 s.f.
(III) A chord is that line in a circle that runs from one point of a circumference to the other without passing the centre. XY, which is a line, follows this definition.